Data Science Interview Questions & Answers (2026)

Use grid search, random search or Bayesian optimisation with cross-validation, starting with a coarse random search and narrowing the promising ranges.

Discriminative models learn P(y given x) directly (logistic regression, SVM). Generative models learn the joint P(x, y) and can generate data (Naive Bayes, GANs).

A table of true positives, false positives, true negatives and false negatives from which accuracy, precision, recall and F1 are calculated.

Both measure node impurity; Gini is cheaper to compute and entropy is slightly more sensitive to class balance, with similar trees in practice.

Tie metrics to business outcomes such as cost saved, show feature importance or SHAP values, give example predictions and be transparent about limitations.

A symmetric bell-shaped distribution defined by mean and standard deviation, where about 68%, 95% and 99.7% of values lie within 1, 2 and 3 standard deviations.

Information from outside the training window, such as future data or test statistics, enters training and inflates performance. Split first, then fit scalers and encoders on training data only.

An epoch is one pass over the training data; a batch is the subset used for one update; an iteration is one weight update on a batch.

Split the data into k folds, train on k−1 folds and validate on the remaining one, rotate and average the scores. It gives a more reliable estimate than one split and helps tune hyperparameters without touching the test set.

Power is the probability of detecting a real effect. Increase it with a larger sample, a bigger effect size, lower noise or a higher significance level.

Calibration checks whether predicted probabilities match real frequencies (e.g. 70% predictions are right about 70% of the time). Fix with Platt scaling or isotonic regression.

Activations add non-linearity so networks can learn complex patterns. ReLU (max(0, x)) is cheap and reduces vanishing gradients compared with sigmoid/tanh; Leaky ReLU avoids 'dead' neurons.

Both measure node impurity; Gini is cheaper to compute and entropy is slightly more sensitive to class balance, with similar trees in practice.

Gradients shrink as they pass through many layers (for example with sigmoid), so early layers barely learn. ReLU, residual connections and good initialisation help.

ReLU for hidden layers, sigmoid for binary outputs, softmax for multi-class outputs and tanh when zero-centred outputs help; Leaky ReLU avoids dead neurons.

Use filter methods (correlation, chi-square), wrapper methods (RFE), embedded methods (Lasso, tree importance) and domain knowledge, validating each choice with cross-validation.

Putting features on comparable ranges using standardisation or min-max scaling. Distance-based and gradient-based models (KNN, SVM, regression, neural nets) need it; tree models do not.

As the number of independent trials grows, the sample average converges to the true expected value, which is why larger samples give more stable estimates.

RNNs process sequences with a hidden state but struggle with long dependencies. LSTMs add gates that control what to remember or forget, easing the vanishing gradient.

Covariance shows the direction of a relationship but depends on units. Correlation is covariance scaled to −1…+1, so it shows direction and strength and is unit-free.

L1 (Lasso) adds absolute weights and can shrink some to zero, giving feature selection. L2 (Ridge) adds squared weights and shrinks them smoothly without removing features.

Use stratified splits, class weights, resampling (SMOTE or undersampling) and threshold tuning, and judge the model with PR-AUC or F1 instead of accuracy.

Parametric tests assume a distribution (usually normal) and use means; non-parametric tests such as Mann-Whitney use ranks and make fewer assumptions.

Predictors that are highly correlated make coefficients unstable. Detect with VIF above about 5-10, then drop or combine features, use PCA or apply regularisation.

A network that compresses inputs into a small latent code and reconstructs them; used for denoising, dimensionality reduction and anomaly detection.

Type I = false positive (rejecting a true null), probability α. Type II = false negative (missing a real effect), probability β. Power = 1 − β.

First understand why data is missing. Then drop rows or columns with too many nulls, impute with mean/median/mode or a model (KNN), add a 'was_missing' flag, and fit imputers on training data only.

Train fits the model, validation tunes hyperparameters and model choice, and the untouched test set gives a final unbiased estimate of performance.

List: ordered and mutable. Tuple: ordered and immutable (hashable, slightly faster). Set: unordered, unique items, fast membership checks. Dict: key–value pairs with fast lookup by key.

== compares values for equality, while is checks whether two names point to the same object in memory. Use is mainly for None checks.

loc selects by label (row and column names, inclusive of the end label); iloc selects by integer position (end-exclusive).

Regression predicts continuous values such as price; classification predicts discrete categories such as spam or not spam.

A shallow copy duplicates the outer object but shares nested objects. A deep copy (copy.deepcopy) recursively duplicates everything, so changes to nested items do not leak.

It assigns points to the nearest centroid and updates centroids until stable. Choose k with the elbow method, silhouette score or business context.

Splitting text into units such as words, subwords or characters that are mapped to ids; subword methods like BPE handle rare words well.

The ROC curve plots true positive rate against false positive rate across thresholds. AUC is the probability that a random positive is ranked above a random negative; 0.5 is chance.

pd.pivot_table(df, index='region', columns='month', values='sales', aggfunc='sum') reshapes long data into a summary matrix; melt() does the reverse.

Precision = TP / (TP + FP). Recall = TP / (TP + FN). Prefer recall when missing a positive is costly — for example disease screening or fraud detection.

A decorator wraps a function to add behaviour such as logging, timing or caching without changing its code. It is applied with the @name syntax above the function.

int, float, complex, bool, str, list, tuple, set, dict and NoneType. Mutable ones are list, set and dict; the others are immutable.

Use the IQR rule (below Q1-1.5 IQR or above Q3+1.5 IQR), z-scores beyond 3, box plots or model-based methods such as Isolation Forest, then decide whether to cap, remove or keep them.

Regularization adds a penalty on weights to reduce overfitting. L1 (Lasso) adds |w| and can push features to exactly zero. L2 (Ridge) adds w² and shrinks weights smoothly.

The probability of seeing a result at least as extreme as the observed one if the null hypothesis were true. A small p-value is evidence against the null, not proof that the alternative is true.

Bagging trains models in parallel on bootstrap samples and averages them (reduces variance, e.g. Random Forest). Boosting trains models one after another, each fixing the previous errors (reduces bias, e.g. XGBoost).

df.drop_duplicates(subset=[...], keep='first') removes repeated rows; use duplicated() first to inspect what will be dropped.

Read in chunks or use usecols and dtypes, convert strings to category, avoid apply with row loops in favour of vectorised ops, and consider Polars, Dask or Parquet storage.

They store same-type values in contiguous memory and run vectorised operations in compiled C, avoiding Python loop overhead and per-object type checks.

A mutex in CPython that lets only one thread execute Python bytecode at a time. Use multiprocessing for CPU-bound work and threads or asyncio for I/O-bound work.

Small anonymous one-line functions, handy as arguments to sort, map, filter or Pandas apply.

Mean is the average, median is the middle value after sorting and mode is the most frequent value. Median is more robust to outliers.

A method is a function that belongs to an object or class and receives the instance (self) as its first argument.

Define churn and the prediction window, build behavioural features, split by time, train and compare models, evaluate with recall and lift, explain drivers and monitor drift after deployment.

It predicts from the k nearest labelled points. It is simple but slow at prediction time, sensitive to scaling and irrelevant features, and weak in high dimensions.

Discriminative models learn P(y given x) directly (logistic regression, SVM). Generative models learn the joint P(x, y) and can generate data (Naive Bayes, GANs).

A decorator wraps a function to add behaviour such as logging, timing or caching without changing its code. It is applied with the @name syntax above the function.

First understand why data is missing. Then drop rows or columns with too many nulls, impute with mean/median/mode or a model (KNN), add a 'was_missing' flag, and fit imputers on training data only.

Regularization adds a penalty on weights to reduce overfitting. L1 (Lasso) adds |w| and can push features to exactly zero. L2 (Ridge) adds w² and shrinks weights smoothly.

*args collects extra positional arguments into a tuple; **kwargs collects extra keyword arguments into a dict. They make function signatures flexible and are common in wrappers and decorators.

Covariance shows the direction of a relationship but depends on units. Correlation is covariance scaled to −1…+1, so it shows direction and strength and is unit-free.

Add a classification head, freeze or gradually unfreeze layers, use a small learning rate, train on labelled data with validation, and track F1 per class.

The rule that lets arrays of different shapes operate together by virtually stretching the smaller one, for example adding a scalar or a (3,) vector to a (4,3) matrix.

The ROC curve plots true positive rate against false positive rate across thresholds. AUC is the probability that a random positive is ranked above a random negative; 0.5 is chance.

Package the model behind an API with versioning, track latency and errors, monitor input drift and prediction quality, and automate retraining with rollback.

merge joins on columns, SQL-style (how='inner', 'left', ...). join joins on the index. concat stacks DataFrames along rows or columns.

Splitting text into units such as words, subwords or characters that are mapped to ids; subword methods like BPE handle rare words well.

A decorator wraps a function to add behaviour such as logging, timing or caching without changing its code. It is applied with the @name syntax above the function.

Frequentists treat parameters as fixed and use long-run frequencies; Bayesians treat parameters as distributions updated with data via priors and posteriors, giving direct probability statements.

Define churn and the prediction window → build usage and billing features → handle imbalance → train gradient boosting → evaluate with PR-AUC and lift → explain with SHAP → deploy as batch scoring or an API → monitor drift → hand top-risk users to the retention team.

Power is the probability of detecting a real effect. Increase it with a larger sample, a bigger effect size, lower noise or a higher significance level.

int, float, complex, bool, str, list, tuple, set, dict and NoneType. Mutable ones are list, set and dict; the others are immutable.

Package the model behind an API with versioning, track latency and errors, monitor input drift and prediction quality, and automate retraining with rollback.

Supervised learning trains on labelled data to predict a target; unsupervised learning finds structure such as clusters or components in unlabelled data.

Small anonymous one-line functions, handy as arguments to sort, map, filter or Pandas apply.

Tie metrics to business outcomes such as cost saved, show feature importance or SHAP values, give example predictions and be transparent about limitations.

The rule that lets arrays of different shapes operate together by virtually stretching the smaller one, for example adding a scalar or a (3,) vector to a (4,3) matrix.

It applies Bayes' theorem assuming features are independent given the class. The assumption is rarely true but the model is fast and works well for text.

Use stratified splits, class weights, resampling such as SMOTE, threshold tuning and judge models with precision, recall, F1 or PR-AUC instead of accuracy.

Use stratified splits, class weights, resampling (SMOTE or undersampling) and threshold tuning, and judge the model with PR-AUC or F1 instead of accuracy.

It models the log-odds of a binary outcome as a linear function and passes it through a sigmoid to give probabilities, trained by maximising likelihood.

A set stores unique values with no keys; a dictionary stores key-value pairs with unique keys. Both use hashing, so lookups are O(1) on average.

Split the data into k folds, train on k−1 folds and validate on the remaining one, rotate and average the scores. It gives a more reliable estimate than one split and helps tune hyperparameters without touching the test set.

Term Frequency × Inverse Document Frequency: a word scores high if it is frequent in one document but rare across all documents. A classic way to turn text into numeric features.

A method is a function that belongs to an object or class and receives the instance (self) as its first argument.

A network that compresses inputs into a small latent code and reconstructs them; used for denoising, dimensionality reduction and anomaly detection.

Training a meta-model on the predictions of several base models, often using cross-validated predictions to avoid leakage.

It normalises layer inputs per mini-batch and then rescales them, stabilising and speeding up training and allowing higher learning rates.

Define the hypothesis and one primary metric, calculate sample size from the baseline, minimum detectable effect, α and power, randomise users, run for full business cycles, check for sample-ratio mismatch, then test both statistical and practical significance.

Retrieval-Augmented Generation fetches relevant documents and gives them to an LLM as context, reducing hallucination and keeping answers grounded in current private data.

Discriminative models learn P(y given x) directly (logistic regression, SVM). Generative models learn the joint P(x, y) and can generate data (Naive Bayes, GANs).

This is overfitting. Check for data leakage, simplify the model, add regularization, get more data or augment it, use cross-validation, early stopping and feature selection.

As the number of independent trials grows, the sample average converges to the true expected value, which is why larger samples give more stable estimates.

RNNs process sequences with a hidden state but struggle with long dependencies. LSTMs add gates that control what to remember or forget, easing the vanishing gradient.

An epoch is one pass over the training data; a batch is the subset used for one update; an iteration is one weight update on a batch.

It computes the gradient of the loss with respect to every weight by applying the chain rule backwards through the network, so gradient descent can update them.

Use stratified splits, class weights, resampling (SMOTE or undersampling) and threshold tuning, and judge the model with PR-AUC or F1 instead of accuracy.

An optimisation method that updates weights in the opposite direction of the loss gradient. The learning rate sets the step size: too high and it diverges, too low and it is slow. Variants include SGD, mini-batch and Adam.

Splitting text into units such as words, subwords or characters that are mapped to ids; subword methods like BPE handle rare words well.

Power is the probability of detecting a real effect. Increase it with a larger sample, a bigger effect size, lower noise or a higher significance level.

Correlation measures linear association between variables (-1 to 1). A third factor, reverse causality or chance can create it, so causation needs controlled experiments.

Pearson measures linear relationships on continuous data; Spearman uses ranks, so it captures monotonic relationships and is less sensitive to outliers.

Define churn and the prediction window → build usage and billing features → handle imbalance → train gradient boosting → evaluate with PR-AUC and lift → explain with SHAP → deploy as batch scoring or an API → monitor drift → hand top-risk users to the retention team.

Use filter methods (correlation, chi-square), wrapper methods (RFE), embedded methods (Lasso, tree importance) and domain knowledge, validating each choice with cross-validation.

Reusing a model pretrained on a large dataset and fine-tuning it on a smaller task-specific dataset, saving data, time and compute.

Measure first with cProfile or timeit, then replace loops with NumPy or Pandas vectorised calls, use built-ins, caching and better data structures.

It normalises layer inputs per mini-batch and then rescales them, stabilising and speeding up training and allowing higher learning rates.

A range built from sample data that would contain the true parameter in a stated percentage (for example 95%) of repeated samples. It is not the probability that the parameter lies inside this one interval.

Training a meta-model on the predictions of several base models, often using cross-validated predictions to avoid leakage.

Define churn and the prediction window, build behavioural features, split by time, train and compare models, evaluate with recall and lift, explain drivers and monitor drift after deployment.

Convolution filters slide over the input to detect local patterns, pooling reduces size, and deeper layers combine edges into shapes and objects. Used mainly for images.

Predictors that are highly correlated make coefficients unstable. Detect with VIF above about 5-10, then drop or combine features, use PCA or apply regularisation.

Putting features on comparable ranges using standardisation or min-max scaling. Distance-based and gradient-based models (KNN, SVM, regression, neural nets) need it; tree models do not.

Define churn and the prediction window → build usage and billing features → handle imbalance → train gradient boosting → evaluate with PR-AUC and lift → explain with SHAP → deploy as batch scoring or an API → monitor drift → hand top-risk users to the retention team.

L1 (Lasso) adds absolute weights and can shrink some to zero, giving feature selection. L2 (Ridge) adds squared weights and shrinks them smoothly without removing features.

Bias is error from overly simple assumptions (underfitting). Variance is sensitivity to the training data (overfitting). More model complexity lowers bias but raises variance — aim for the lowest total error using cross-validation and regularization.

Retrieval-Augmented Generation fetches relevant documents and gives them to an LLM as context, reducing hallucination and keeping answers grounded in current private data.

CNNs use convolutions to find spatial patterns (images). RNNs/LSTMs process sequences step by step but struggle with long context. Transformers use self-attention to look at all tokens at once — parallel and better at long-range context; they power modern LLMs.

Add a classification head, freeze or gradually unfreeze layers, use a small learning rate, train on labelled data with validation, and track F1 per class.

Calibration checks whether predicted probabilities match real frequencies (e.g. 70% predictions are right about 70% of the time). Fix with Platt scaling or isotonic regression.

A decorator wraps a function to add behaviour such as logging, timing or caching without changing its code. It is applied with the @name syntax above the function.

A function using yield that produces values lazily, one at a time. It saves memory when processing large files or streams because the full sequence is never held in RAM.

Split the data into k folds, train on k−1 folds and validate on the remaining one, rotate and average the scores. It gives a more reliable estimate than one split and helps tune hyperparameters without touching the test set.

A measure of asymmetry. Right-skewed data has a long tail on the right (mean greater than median); left-skewed is the opposite. Log transforms often reduce right skew.

Type I = false positive (rejecting a true null), probability α. Type II = false negative (missing a real effect), probability β. Power = 1 − β.

They build a list in one readable expression, for example [x*x for x in data if x > 0]. They are usually faster than an equivalent for-loop with append.

Use grid search, random search or Bayesian optimisation with cross-validation, starting with a coarse random search and narrowing the promising ranges.

Frequentists treat parameters as fixed and use long-run frequencies; Bayesians treat parameters as distributions updated with data via priors and posteriors, giving direct probability statements.

An optimisation method that updates weights in the opposite direction of the loss gradient. The learning rate sets the step size: too high and it diverges, too low and it is slow. Variants include SGD, mini-batch and Adam.

A set stores unique values with no keys; a dictionary stores key-value pairs with unique keys. Both use hashing, so lookups are O(1) on average.

It assigns points to the nearest centroid and updates centroids until stable. Choose k with the elbow method, silhouette score or business context.

It normalises layer inputs per mini-batch and then rescales them, stabilising and speeding up training and allowing higher learning rates.

Use stratified splits, class weights, resampling such as SMOTE, threshold tuning and judge models with precision, recall, F1 or PR-AUC instead of accuracy.

Precision = TP / (TP + FP). Recall = TP / (TP + FN). Prefer recall when missing a positive is costly — for example disease screening or fraud detection.

List: ordered and mutable. Tuple: ordered and immutable (hashable, slightly faster). Set: unordered, unique items, fast membership checks. Dict: key–value pairs with fast lookup by key.

Use target or frequency encoding with cross-validation, hashing, embeddings or grouping rare categories, instead of huge one-hot matrices.

Correlation measures linear association between variables (-1 to 1). A third factor, reverse causality or chance can create it, so causation needs controlled experiments.

It projects data onto orthogonal directions of maximum variance to reduce dimensions, remove correlation and speed up models, at some cost of interpretability.

The ROC curve plots true positive rate against false positive rate across thresholds. AUC is the probability that a random positive is ranked above a random negative; 0.5 is chance.

Regularization adds a penalty on weights to reduce overfitting. L1 (Lasso) adds |w| and can push features to exactly zero. L2 (Ridge) adds w² and shrinks weights smoothly.

Precision = TP / (TP + FP). Recall = TP / (TP + FN). Prefer recall when missing a positive is costly — for example disease screening or fraud detection.

Modelling the count of events in a fixed interval when events occur independently at a constant average rate, such as calls per hour or defects per batch.

This is overfitting. Check for data leakage, simplify the model, add regularization, get more data or augment it, use cross-validation, early stopping and feature selection.

Accuracy, F1 and confusion matrices for classification, BLEU or ROUGE for generation and summarisation, perplexity for language models, plus human review.

Parametric tests assume a distribution (usually normal) and use means; non-parametric tests such as Mann-Whitney use ranks and make fewer assumptions.

Use stratified splits, class weights, resampling (SMOTE or undersampling) and threshold tuning, and judge the model with PR-AUC or F1 instead of accuracy.

A symmetric bell-shaped distribution defined by mean and standard deviation, where about 68%, 95% and 99.7% of values lie within 1, 2 and 3 standard deviations.

merge joins on columns, SQL-style (how='inner', 'left', ...). join joins on the index. concat stacks DataFrames along rows or columns.

Calibration checks whether predicted probabilities match real frequencies (e.g. 70% predictions are right about 70% of the time). Fix with Platt scaling or isotonic regression.

Package the model behind an API with versioning, track latency and errors, monitor input drift and prediction quality, and automate retraining with rollback.

The square root of the variance; it measures how far values typically sit from the mean, in the same units as the data.

Supervised learning trains on labelled data to predict a target; unsupervised learning finds structure such as clusters or components in unlabelled data.

Transformers use self-attention to process all tokens in parallel and capture long-range context, making them faster to train and more scalable than sequential RNNs.

A method is a function that belongs to an object or class and receives the instance (self) as its first argument.

Correlation measures linear association between variables (-1 to 1). A third factor, reverse causality or chance can create it, so causation needs controlled experiments.

Bias is error from overly simple assumptions (underfitting). Variance is sensitivity to the training data (overfitting). More model complexity lowers bias but raises variance — aim for the lowest total error using cross-validation and regularization.

Split the data into k folds, train on k−1 folds and validate on the remaining one, rotate and average the scores. It gives a more reliable estimate than one split and helps tune hyperparameters without touching the test set.

An iterable can produce an iterator (it has __iter__); an iterator has __next__ and remembers its position. A for-loop calls iter() on the iterable and then next() repeatedly.

Predictors that are highly correlated make coefficients unstable. Detect with VIF above about 5-10, then drop or combine features, use PCA or apply regularisation.

Use the IQR rule (below Q1-1.5 IQR or above Q3+1.5 IQR), z-scores beyond 3, box plots or model-based methods such as Isolation Forest, then decide whether to cap, remove or keep them.

Add a classification head, freeze or gradually unfreeze layers, use a small learning rate, train on labelled data with validation, and track F1 per class.

A mutex in CPython that lets only one thread execute Python bytecode at a time. Use multiprocessing for CPU-bound work and threads or asyncio for I/O-bound work.

df.drop_duplicates(subset=[...], keep='first') removes repeated rows; use duplicated() first to inspect what will be dropped.

A symmetric bell-shaped distribution defined by mean and standard deviation, where about 68%, 95% and 99.7% of values lie within 1, 2 and 3 standard deviations.

Training a meta-model on the predictions of several base models, often using cross-validated predictions to avoid leakage.

Splitting text into units such as words, subwords or characters that are mapped to ids; subword methods like BPE handle rare words well.

A decorator wraps a function to add behaviour such as logging, timing or caching without changing its code. It is applied with the @name syntax above the function.

A forest averages many trees trained on bootstrapped rows and random feature subsets, which cuts variance and overfitting at the cost of interpretability.

A network that compresses inputs into a small latent code and reconstructs them; used for denoising, dimensionality reduction and anomaly detection.

Frequentists treat parameters as fixed and use long-run frequencies; Bayesians treat parameters as distributions updated with data via priors and posteriors, giving direct probability statements.

The probability of seeing a result at least as extreme as the observed one if the null hypothesis were true. A small p-value is evidence against the null, not proof that the alternative is true.

A set stores unique values with no keys; a dictionary stores key-value pairs with unique keys. Both use hashing, so lookups are O(1) on average.

Use stratified splits, class weights, resampling such as SMOTE, threshold tuning and judge models with precision, recall, F1 or PR-AUC instead of accuracy.

CNNs use convolutions to find spatial patterns (images). RNNs/LSTMs process sequences step by step but struggle with long context. Transformers use self-attention to look at all tokens at once — parallel and better at long-range context; they power modern LLMs.

Tie metrics to business outcomes such as cost saved, show feature importance or SHAP values, give example predictions and be transparent about limitations.

It normalises layer inputs per mini-batch and then rescales them, stabilising and speeding up training and allowing higher learning rates.

Small anonymous one-line functions, handy as arguments to sort, map, filter or Pandas apply.

Define churn and the prediction window → build usage and billing features → handle imbalance → train gradient boosting → evaluate with PR-AUC and lift → explain with SHAP → deploy as batch scoring or an API → monitor drift → hand top-risk users to the retention team.

Putting features on comparable ranges using standardisation or min-max scaling. Distance-based and gradient-based models (KNN, SVM, regression, neural nets) need it; tree models do not.

loc selects by label (row and column names, inclusive of the end label); iloc selects by integer position (end-exclusive).

RNNs process sequences with a hidden state but struggle with long dependencies. LSTMs add gates that control what to remember or forget, easing the vanishing gradient.

The model memorises noise and fails on new data. Prevent it with more data, simpler models, regularisation, cross-validation, early stopping and dropout.

pd.pivot_table(df, index='region', columns='month', values='sales', aggfunc='sum') reshapes long data into a summary matrix; melt() does the reverse.

Both measure node impurity; Gini is cheaper to compute and entropy is slightly more sensitive to class balance, with similar trees in practice.

Accuracy, F1 and confusion matrices for classification, BLEU or ROUGE for generation and summarisation, perplexity for language models, plus human review.

Term Frequency × Inverse Document Frequency: a word scores high if it is frequent in one document but rare across all documents. A classic way to turn text into numeric features.

df.drop_duplicates(subset=[...], keep='first') removes repeated rows; use duplicated() first to inspect what will be dropped.

Bias is error from overly simple assumptions (underfitting). Variance is sensitivity to the training data (overfitting). More model complexity lowers bias but raises variance — aim for the lowest total error using cross-validation and regularization.

Measure first with cProfile or timeit, then replace loops with NumPy or Pandas vectorised calls, use built-ins, caching and better data structures.

A shallow copy duplicates the outer object but shares nested objects. A deep copy (copy.deepcopy) recursively duplicates everything, so changes to nested items do not leak.

The probability of seeing a result at least this extreme if the null hypothesis were true. A small p-value (for example < 0.05) is evidence against the null hypothesis.

Use filter methods (correlation, chi-square), wrapper methods (RFE), embedded methods (Lasso, tree importance) and domain knowledge, validating each choice with cross-validation.

The model memorises noise and fails on new data. Prevent it with more data, simpler models, regularisation, cross-validation, early stopping and dropout.

L1 (Lasso) adds absolute weights and can shrink some to zero, giving feature selection. L2 (Ridge) adds squared weights and shrinks them smoothly without removing features.

An epoch is one pass over the training data; a batch is the subset used for one update; an iteration is one weight update on a batch.

A function using yield that produces values lazily, one at a time. It saves memory when processing large files or streams because the full sequence is never held in RAM.

It combines gradient boosting with regularisation, handling of missing values, parallel tree construction and speed optimisations, and it performs strongly on tabular data.

== compares values for equality, while is checks whether two names point to the same object in memory. Use is mainly for None checks.

Regularization adds a penalty on weights to reduce overfitting. L1 (Lasso) adds |w| and can push features to exactly zero. L2 (Ridge) adds w² and shrinks weights smoothly.

Read in chunks or use usecols and dtypes, convert strings to category, avoid apply with row loops in favour of vectorised ops, and consider Polars, Dask or Parquet storage.

Pearson measures linear relationships on continuous data; Spearman uses ranks, so it captures monotonic relationships and is less sensitive to outliers.

It assigns points to the nearest centroid and updates centroids until stable. Choose k with the elbow method, silhouette score or business context.

The probability of seeing a result at least as extreme as the observed one if the null hypothesis were true. A small p-value is evidence against the null, not proof that the alternative is true.

Information from outside the training window, such as future data or test statistics, enters training and inflates performance. Split first, then fit scalers and encoders on training data only.

Transformers use self-attention to process all tokens in parallel and capture long-range context, making them faster to train and more scalable than sequential RNNs.

CNNs use convolutions to find spatial patterns (images). RNNs/LSTMs process sequences step by step but struggle with long context. Transformers use self-attention to look at all tokens at once — parallel and better at long-range context; they power modern LLMs.

map works element-wise on a Series, apply works on a Series or along a DataFrame axis, and applymap (now DataFrame.map) applies a function to every cell.

Bias occurs when the sample does not represent the population. Reduce it with random or stratified sampling, higher response rates and by checking sample demographics against the population.

Regression predicts continuous values such as price; classification predicts discrete categories such as spam or not spam.

An iterable can produce an iterator (it has __iter__); an iterator has __next__ and remembers its position. A for-loop calls iter() on the iterable and then next() repeatedly.

The rule that lets arrays of different shapes operate together by virtually stretching the smaller one, for example adding a scalar or a (3,) vector to a (4,3) matrix.

It normalises layer inputs per mini-batch and then rescales them, stabilising and speeding up training and allowing higher learning rates.

*args collects extra positional arguments into a tuple; **kwargs collects extra keyword arguments into a dict. They make function signatures flexible and are common in wrappers and decorators.

Use target or frequency encoding with cross-validation, hashing, embeddings or grouping rare categories, instead of huge one-hot matrices.

Bagging trains models in parallel on bootstrap samples and averages them (reduces variance, e.g. Random Forest). Boosting trains models one after another, each fixing the previous errors (reduces bias, e.g. XGBoost).

A symmetric bell-shaped distribution defined by mean and standard deviation, where about 68%, 95% and 99.7% of values lie within 1, 2 and 3 standard deviations.

Use stratified splits, class weights, resampling such as SMOTE, threshold tuning and judge models with precision, recall, F1 or PR-AUC instead of accuracy.

Bias is error from overly simple assumptions (underfitting). Variance is sensitivity to the training data (overfitting). More model complexity lowers bias but raises variance — aim for the lowest total error using cross-validation and regularization.

An epoch is one pass over the training data; a batch is the subset used for one update; an iteration is one weight update on a batch.

Define the hypothesis and one primary metric, calculate sample size from the baseline, minimum detectable effect, α and power, randomise users, run for full business cycles, check for sample-ratio mismatch, then test both statistical and practical significance.

The ROC curve plots true positive rate against false positive rate across thresholds. AUC is the probability that a random positive is ranked above a random negative; 0.5 is chance.

Use the IQR rule (below Q1-1.5 IQR or above Q3+1.5 IQR), z-scores beyond 3, box plots or model-based methods such as Isolation Forest, then decide whether to cap, remove or keep them.

Add a classification head, freeze or gradually unfreeze layers, use a small learning rate, train on labelled data with validation, and track F1 per class.

Regression predicts continuous values such as price; classification predicts discrete categories such as spam or not spam.

Predictors that are highly correlated make coefficients unstable. Detect with VIF above about 5-10, then drop or combine features, use PCA or apply regularisation.

Layers of connected neurons that apply weights, biases and activation functions to learn complex patterns, trained by backpropagation.

Precision = TP / (TP + FP). Recall = TP / (TP + FN). Prefer recall when missing a positive is costly — for example disease screening or fraud detection.

It projects data onto orthogonal directions of maximum variance to reduce dimensions, remove correlation and speed up models, at some cost of interpretability.

It tries candidate splits and picks the one that most reduces impurity — Gini or entropy (information gain) for classification, variance / MSE for regression.

Activations add non-linearity so networks can learn complex patterns. ReLU (max(0, x)) is cheap and reduces vanishing gradients compared with sigmoid/tanh; Leaky ReLU avoids 'dead' neurons.

RNNs process sequences with a hidden state but struggle with long dependencies. LSTMs add gates that control what to remember or forget, easing the vanishing gradient.

Read in chunks or use usecols and dtypes, convert strings to category, avoid apply with row loops in favour of vectorised ops, and consider Polars, Dask or Parquet storage.

Monitor input distributions and live metrics, compare to training baselines, and retrain or recalibrate on fresh data when performance drops.

A table of true positives, false positives, true negatives and false negatives from which accuracy, precision, recall and F1 are calculated.

The model memorises noise and fails on new data. Prevent it with more data, simpler models, regularisation, cross-validation, early stopping and dropout.

Gradients shrink as they pass through many layers (for example with sigmoid), so early layers barely learn. ReLU, residual connections and good initialisation help.

loc selects by label (row and column names, inclusive of the end label); iloc selects by integer position (end-exclusive).

int, float, complex, bool, str, list, tuple, set, dict and NoneType. Mutable ones are list, set and dict; the others are immutable.

The probability of seeing a result at least as extreme as the observed one if the null hypothesis were true. A small p-value is evidence against the null, not proof that the alternative is true.

Convolution filters slide over the input to detect local patterns, pooling reduces size, and deeper layers combine edges into shapes and objects. Used mainly for images.

Covariance shows the direction of a relationship but depends on units. Correlation is covariance scaled to −1…+1, so it shows direction and strength and is unit-free.

The probability of seeing a result at least this extreme if the null hypothesis were true. A small p-value (for example < 0.05) is evidence against the null hypothesis.

A forest averages many trees trained on bootstrapped rows and random feature subsets, which cuts variance and overfitting at the cost of interpretability.

It fits a line minimising squared error. Assumes linearity, independent errors, constant variance (homoscedasticity), normally distributed residuals and no strong multicollinearity.

Splitting text into units such as words, subwords or characters that are mapped to ids; subword methods like BPE handle rare words well.

Use filter methods (correlation, chi-square), wrapper methods (RFE), embedded methods (Lasso, tree importance) and domain knowledge, validating each choice with cross-validation.

Discriminative models learn P(y given x) directly (logistic regression, SVM). Generative models learn the joint P(x, y) and can generate data (Naive Bayes, GANs).

It lets a model weigh which input positions matter most for each output, computing weighted combinations of values from query-key similarity. It is the core of transformers.

ReLU for hidden layers, sigmoid for binary outputs, softmax for multi-class outputs and tanh when zero-centred outputs help; Leaky ReLU avoids dead neurons.

They build a list in one readable expression, for example [x*x for x in data if x > 0]. They are usually faster than an equivalent for-loop with append.

It computes the gradient of the loss with respect to every weight by applying the chain rule backwards through the network, so gradient descent can update them.

Use stratified splits, class weights, resampling (SMOTE or undersampling) and threshold tuning, and judge the model with PR-AUC or F1 instead of accuracy.

Mean is the average, median is the middle value after sorting and mode is the most frequent value. Median is more robust to outliers.

Define churn and the prediction window, build behavioural features, split by time, train and compare models, evaluate with recall and lift, explain drivers and monitor drift after deployment.

map works element-wise on a Series, apply works on a Series or along a DataFrame axis, and applymap (now DataFrame.map) applies a function to every cell.

== compares values for equality, while is checks whether two names point to the same object in memory. Use is mainly for None checks.

Use grid search, random search or Bayesian optimisation with cross-validation, starting with a coarse random search and narrowing the promising ranges.

Modelling the count of events in a fixed interval when events occur independently at a constant average rate, such as calls per hour or defects per batch.

SVM finds the maximum-margin separating hyperplane. Kernels such as RBF compute similarity in a higher-dimensional space implicitly, so non-linear boundaries are possible.

Correlation measures linear association between variables (-1 to 1). A third factor, reverse causality or chance can create it, so causation needs controlled experiments.

An optimisation method that updates weights in the opposite direction of the loss gradient. The learning rate sets the step size: too high and it diverges, too low and it is slow. Variants include SGD, mini-batch and Adam.

Accuracy, F1 and confusion matrices for classification, BLEU or ROUGE for generation and summarisation, perplexity for language models, plus human review.

It checks whether observed category counts differ from expected counts, used for independence between two categorical variables and for goodness of fit.

A range built from sample data that would contain the true parameter in a stated percentage (for example 95%) of repeated samples. It is not the probability that the parameter lies inside this one interval.

A mutex in CPython that lets only one thread execute Python bytecode at a time. Use multiprocessing for CPU-bound work and threads or asyncio for I/O-bound work.

An iterable can produce an iterator (it has __iter__); an iterator has __next__ and remembers its position. A for-loop calls iter() on the iterable and then next() repeatedly.

Term Frequency × Inverse Document Frequency: a word scores high if it is frequent in one document but rare across all documents. A classic way to turn text into numeric features.

Power is the probability of detecting a real effect. Increase it with a larger sample, a bigger effect size, lower noise or a higher significance level.

Package the model behind an API with versioning, track latency and errors, monitor input drift and prediction quality, and automate retraining with rollback.

df.drop_duplicates(subset=[...], keep='first') removes repeated rows; use duplicated() first to inspect what will be dropped.

It applies Bayes' theorem assuming features are independent given the class. The assumption is rarely true but the model is fast and works well for text.

Both measure node impurity; Gini is cheaper to compute and entropy is slightly more sensitive to class balance, with similar trees in practice.

Bias occurs when the sample does not represent the population. Reduce it with random or stratified sampling, higher response rates and by checking sample demographics against the population.

A function using yield that produces values lazily, one at a time. It saves memory when processing large files or streams because the full sequence is never held in RAM.

Transformers use self-attention to process all tokens in parallel and capture long-range context, making them faster to train and more scalable than sequential RNNs.

Reusing a model pretrained on a large dataset and fine-tuning it on a smaller task-specific dataset, saving data, time and compute.

First understand why data is missing. Then drop rows or columns with too many nulls, impute with mean/median/mode or a model (KNN), add a 'was_missing' flag, and fit imputers on training data only.

Train fits the model, validation tunes hyperparameters and model choice, and the untouched test set gives a final unbiased estimate of performance.

P(A given B) = P(B given A) x P(A) / P(B). In a medical test it converts test accuracy and disease prevalence into the real chance a positive result means disease.

Regularization adds a penalty on weights to reduce overfitting. L1 (Lasso) adds |w| and can push features to exactly zero. L2 (Ridge) adds w² and shrinks weights smoothly.

It assigns points to the nearest centroid and updates centroids until stable. Choose k with the elbow method, silhouette score or business context.

Calibration checks whether predicted probabilities match real frequencies (e.g. 70% predictions are right about 70% of the time). Fix with Platt scaling or isotonic regression.

Type I = false positive (rejecting a true null), probability α. Type II = false negative (missing a real effect), probability β. Power = 1 − β.

The square root of the variance; it measures how far values typically sit from the mean, in the same units as the data.

Define churn and the prediction window, build behavioural features, split by time, train and compare models, evaluate with recall and lift, explain drivers and monitor drift after deployment.

Regularization adds a penalty on weights to reduce overfitting. L1 (Lasso) adds |w| and can push features to exactly zero. L2 (Ridge) adds w² and shrinks weights smoothly.

Training a meta-model on the predictions of several base models, often using cross-validated predictions to avoid leakage.

The probability of seeing a result at least as extreme as the observed one if the null hypothesis were true. A small p-value is evidence against the null, not proof that the alternative is true.

== compares values for equality, while is checks whether two names point to the same object in memory. Use is mainly for None checks.

A function using yield that produces values lazily, one at a time. It saves memory when processing large files or streams because the full sequence is never held in RAM.

*args collects extra positional arguments into a tuple; **kwargs collects extra keyword arguments into a dict. They make function signatures flexible and are common in wrappers and decorators.

map works element-wise on a Series, apply works on a Series or along a DataFrame axis, and applymap (now DataFrame.map) applies a function to every cell.

An epoch is one pass over the training data; a batch is the subset used for one update; an iteration is one weight update on a batch.

Regression predicts continuous values such as price; classification predicts discrete categories such as spam or not spam.

Modelling the count of events in a fixed interval when events occur independently at a constant average rate, such as calls per hour or defects per batch.

It computes the gradient of the loss with respect to every weight by applying the chain rule backwards through the network, so gradient descent can update them.

Predictors that are highly correlated make coefficients unstable. Detect with VIF above about 5-10, then drop or combine features, use PCA or apply regularisation.

Tie metrics to business outcomes such as cost saved, show feature importance or SHAP values, give example predictions and be transparent about limitations.

P(A given B) = P(B given A) x P(A) / P(B). In a medical test it converts test accuracy and disease prevalence into the real chance a positive result means disease.

merge joins on columns, SQL-style (how='inner', 'left', ...). join joins on the index. concat stacks DataFrames along rows or columns.

A shallow copy duplicates the outer object but shares nested objects. A deep copy (copy.deepcopy) recursively duplicates everything, so changes to nested items do not leak.

A measure of asymmetry. Right-skewed data has a long tail on the right (mean greater than median); left-skewed is the opposite. Log transforms often reduce right skew.

loc selects by label (row and column names, inclusive of the end label); iloc selects by integer position (end-exclusive).

They store same-type values in contiguous memory and run vectorised operations in compiled C, avoiding Python loop overhead and per-object type checks.

Activations add non-linearity so networks can learn complex patterns. ReLU (max(0, x)) is cheap and reduces vanishing gradients compared with sigmoid/tanh; Leaky ReLU avoids 'dead' neurons.

Package the model behind an API with versioning, track latency and errors, monitor input drift and prediction quality, and automate retraining with rollback.

Use stratified splits, class weights, resampling such as SMOTE, threshold tuning and judge models with precision, recall, F1 or PR-AUC instead of accuracy.

Use filter methods (correlation, chi-square), wrapper methods (RFE), embedded methods (Lasso, tree importance) and domain knowledge, validating each choice with cross-validation.

Splitting text into units such as words, subwords or characters that are mapped to ids; subword methods like BPE handle rare words well.

Discriminative models learn P(y given x) directly (logistic regression, SVM). Generative models learn the joint P(x, y) and can generate data (Naive Bayes, GANs).

It assigns points to the nearest centroid and updates centroids until stable. Choose k with the elbow method, silhouette score or business context.

First understand why data is missing. Then drop rows or columns with too many nulls, impute with mean/median/mode or a model (KNN), add a 'was_missing' flag, and fit imputers on training data only.

RNNs process sequences with a hidden state but struggle with long dependencies. LSTMs add gates that control what to remember or forget, easing the vanishing gradient.

Use the IQR rule (below Q1-1.5 IQR or above Q3+1.5 IQR), z-scores beyond 3, box plots or model-based methods such as Isolation Forest, then decide whether to cap, remove or keep them.

List: ordered and mutable. Tuple: ordered and immutable (hashable, slightly faster). Set: unordered, unique items, fast membership checks. Dict: key–value pairs with fast lookup by key.

Use stratified splits, class weights, resampling (SMOTE or undersampling) and threshold tuning, and judge the model with PR-AUC or F1 instead of accuracy.

A range built from sample data that would contain the true parameter in a stated percentage (for example 95%) of repeated samples. It is not the probability that the parameter lies inside this one interval.

Both measure node impurity; Gini is cheaper to compute and entropy is slightly more sensitive to class balance, with similar trees in practice.

CNNs use convolutions to find spatial patterns (images). RNNs/LSTMs process sequences step by step but struggle with long context. Transformers use self-attention to look at all tokens at once — parallel and better at long-range context; they power modern LLMs.

Frequentists treat parameters as fixed and use long-run frequencies; Bayesians treat parameters as distributions updated with data via priors and posteriors, giving direct probability statements.

Parametric tests assume a distribution (usually normal) and use means; non-parametric tests such as Mann-Whitney use ranks and make fewer assumptions.

int, float, complex, bool, str, list, tuple, set, dict and NoneType. Mutable ones are list, set and dict; the others are immutable.

df.drop_duplicates(subset=[...], keep='first') removes repeated rows; use duplicated() first to inspect what will be dropped.

It lets a model weigh which input positions matter most for each output, computing weighted combinations of values from query-key similarity. It is the core of transformers.

A forest averages many trees trained on bootstrapped rows and random feature subsets, which cuts variance and overfitting at the cost of interpretability.

Use grid search, random search or Bayesian optimisation with cross-validation, starting with a coarse random search and narrowing the promising ranges.

The rule that lets arrays of different shapes operate together by virtually stretching the smaller one, for example adding a scalar or a (3,) vector to a (4,3) matrix.

Raising the threshold improves precision but lowers recall. Fraud detection leans to recall, while spam filters often prefer precision; choose by the cost of each error.

An iterable can produce an iterator (it has __iter__); an iterator has __next__ and remembers its position. A for-loop calls iter() on the iterable and then next() repeatedly.

Accuracy, F1 and confusion matrices for classification, BLEU or ROUGE for generation and summarisation, perplexity for language models, plus human review.

An optimisation method that updates weights in the opposite direction of the loss gradient. The learning rate sets the step size: too high and it diverges, too low and it is slow. Variants include SGD, mini-batch and Adam.

Precision = TP / (TP + FP). Recall = TP / (TP + FN). Prefer recall when missing a positive is costly — for example disease screening or fraud detection.

It tries candidate splits and picks the one that most reduces impurity — Gini or entropy (information gain) for classification, variance / MSE for regression.

The model memorises noise and fails on new data. Prevent it with more data, simpler models, regularisation, cross-validation, early stopping and dropout.

They build a list in one readable expression, for example [x*x for x in data if x > 0]. They are usually faster than an equivalent for-loop with append.

Mean is the average, median is the middle value after sorting and mode is the most frequent value. Median is more robust to outliers.

The distribution of sample means approaches a normal distribution as the sample size grows (roughly 30+), whatever the population's shape. It lets us build confidence intervals and run hypothesis tests on means.

As the number of independent trials grows, the sample average converges to the true expected value, which is why larger samples give more stable estimates.

Splitting text into units such as words, subwords or characters that are mapped to ids; subword methods like BPE handle rare words well.

Information from outside the training window, such as future data or test statistics, enters training and inflates performance. Split first, then fit scalers and encoders on training data only.

A network that compresses inputs into a small latent code and reconstructs them; used for denoising, dimensionality reduction and anomaly detection.

An iterable can produce an iterator (it has __iter__); an iterator has __next__ and remembers its position. A for-loop calls iter() on the iterable and then next() repeatedly.

Gradients shrink as they pass through many layers (for example with sigmoid), so early layers barely learn. ReLU, residual connections and good initialisation help.

Pearson measures linear relationships on continuous data; Spearman uses ranks, so it captures monotonic relationships and is less sensitive to outliers.

Define the hypothesis and one primary metric, calculate sample size from the baseline, minimum detectable effect, α and power, randomise users, run for full business cycles, check for sample-ratio mismatch, then test both statistical and practical significance.

CNNs use convolutions to find spatial patterns (images). RNNs/LSTMs process sequences step by step but struggle with long context. Transformers use self-attention to look at all tokens at once — parallel and better at long-range context; they power modern LLMs.

SVM finds the maximum-margin separating hyperplane. Kernels such as RBF compute similarity in a higher-dimensional space implicitly, so non-linear boundaries are possible.

Start with a sensible default such as 1e-3 for Adam, run a learning-rate range test, and use schedulers or warm-up while watching the loss curve.