ML Interview Q Series: Is it possible to reformulate a regression task as classification, and can a classification task be turned into a regression problem?

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Comprehensive Explanation

Converting regression to classification or the other way around is typically about adjusting how the output variable is interpreted and how the model is trained:

Turning a Regression Task into Classification

When dealing with a regression problem, your target is a continuous variable (for example, predicting house prices). To convert it into a classification setup, you must discretize this continuous output into categories. A few typical approaches:

Binning

You create intervals or “bins” that partition the continuous output range into classes. For instance, if you have house prices ranging from 100k to 1M, you might define bins: “low-price,” “medium-price,” and “high-price.” Each bin becomes its own category.

Threshold-Based Approach

In a scenario that requires a binary classification, you define a specific threshold on the regression output. For example, in credit scoring, if the regression model predicts the probability of default, you can label any prediction above 0.5 as “high risk” (class 1) and below 0.5 as “low risk” (class 0).

This transformation is straightforward but can introduce information loss because continuous nuances get grouped into discrete buckets. The choice of thresholds or bin boundaries strongly affects performance, and you must ensure that the bins or thresholds are chosen with domain knowledge.

Turning a Classification Task into Regression

In classification, the target is categorical (like “cat,” “dog,” or “bird”). To switch this into a regression formulation, you map each category to a numeric label. For example, you can assign “cat” -> 0, “dog” -> 1, “bird” -> 2 and then predict a real-valued output. The model is thus trained to predict a continuous number that is interpreted as the numeric label for the class. After prediction, you can map the numeric output back to the discrete class by rounding or using the nearest integer.

In practice, you might do something akin to ordinal regression if the categories have an inherent ordering, like “small,” “medium,” and “large.” However, you must consider that not all classification problems have a natural ordering. Mapping classes arbitrarily to numeric values might be less meaningful. Furthermore, standard regression losses might not align well with the classification goal.

Example in Python

import pandas as pd
import numpy as np

# Suppose we have a regression dataset with a continuous target: 'price'
df = pd.DataFrame({
    'feature1': [2.3, 1.2, 5.6, 3.3],
    'feature2': [0.1, 0.7, 0.4, 0.9],
    'price': [100000, 200000, 700000, 400000]
})

# 1) Converting regression (price) into classification using bins
bins = [0, 200000, 500000, np.inf]  # intervals
labels = ['low', 'medium', 'high']
df['price_category'] = pd.cut(df['price'], bins=bins, labels=labels)

# 2) Converting classification into regression by mapping classes to numbers
class_mapping = {'low': 0, 'medium': 1, 'high': 2}
df['numeric_label'] = df['price_category'].map(class_mapping)

print(df)

This code snippet first creates classification labels (low, medium, high) from a continuous price variable. Then it maps those category labels back to numeric codes. In real-world usage, you would train separate models for each step: a classifier for the binned labels or a regressor that predicts numeric codes.

Potential Pitfalls and Considerations

When you bin continuous data, the choice of bin boundaries can alter performance drastically. If bins are not well-chosen, you might end up with imbalanced categories or lose important granularity.

When converting classification to regression by assigning numeric values, the model might assume that the difference between class 0 and class 1 is the same as between class 1 and class 2, which might not be meaningful unless the classes are ordinal. Also, typical regression metrics (like mean squared error) might not reflect classification performance well.

When deciding how to transform one problem type to another, reflect on:

• The loss of information introduced by binning or mapping.

• Whether the classes have an inherent order.

• The proper metrics and training objectives.

• How interpretability and performance trade-offs affect the final goal.

What are some real-world scenarios where converting regression into classification is practical?

One realistic scenario is credit risk modeling. Instead of outputting a continuous risk score from 0 to 1, a bank might categorize borrowers into “low,” “medium,” and “high” risk for quick decision-making. Another example is weather forecasting, where a continuous temperature prediction could be turned into discrete categories like “cool,” “moderate,” and “hot” for simpler reporting. These transformations can make outputs more interpretable for non-technical stakeholders, though you lose some resolution.

How do you select bin thresholds when turning a continuous target into classification labels?

Choosing bin boundaries typically requires domain expertise and data exploration. You might look at the distribution of the target values—if they cluster in certain regions, you might place boundaries around those clusters. Alternatively, you can choose quantiles so that each bin contains roughly the same number of examples, preventing imbalance. However, if the domain suggests natural cutoffs (for instance, specific temperature boundaries for comfort levels), use those. Avoid arbitrary cutoffs that produce extremely skewed or unbalanced bins.

Are there specific performance metrics to watch out for after converting between regression and classification?

Yes, once you do a conversion:

• If you turn regression into classification, you generally use accuracy, precision, recall, F1, or AUC. But the exact choice depends on the application. A threshold-based approach might need calibration to get balanced performance metrics.

• If you turn classification into regression, you might monitor mean squared error, mean absolute error, or R-squared on the numeric labels. But these may not correspond well to classification performance like accuracy, especially if the assigned numeric values do not reflect true ordinal relationships.

How do you handle edge cases or borderline decisions in threshold-based approaches for regression to classification?

When the predicted value is near the threshold, small changes in the input can flip the classification outcome. To mitigate this, you can:

• Introduce a “buffer zone” (e.g., if the threshold is 0.5, consider 0.45–0.55 uncertain and require additional checks).

• Use probabilistic approaches, such as calibrating a confidence interval around the estimate, or adjusting classification based on cost-sensitive decisions.

• Explore multiple threshold values and pick the one that optimizes a chosen metric like F1 or ROC AUC.

Could mapping a classification problem to regression ever be more beneficial than simply modeling classification directly?

This strategy can sometimes work if there is a natural ordinal relationship among the labels. For instance, in satisfaction ratings like “very unhappy,” “unhappy,” “neutral,” “happy,” and “very happy,” assigning numeric labels 1 to 5 could let you use regression and leverage the continuous structure. However, if labels do not have a natural ordering, imposing a numeric scale might add confusion. Also, standard classification models might do better when the classes are purely categorical with no ordinal structure.

How does one decide which architecture or algorithm to use after performing these transformations?

It depends on how you’ve transformed the labels:

• For regression to classification, you typically use classification algorithms like logistic regression, random forest classifier, or neural networks with a softmax (for multiple classes) or sigmoid (for binary classes) output layer.

• For classification to regression, you might use linear regression, random forest regressor, or any regression-capable neural network with a single linear output.

In deep learning, the final layer’s activation function is crucial. For classification tasks (like a binned continuous variable), you use softmax or sigmoid to produce probabilities. For numeric labels, you keep a linear output layer and optimize a regression loss (like mean squared error).

Could you provide more detail on the threshold-based approach in terms of logistic function?

If you use logistic regression for a binary task, the model computes the log-odds of the probability of the positive class. The output is a continuous value between 0 and 1, often denoted y. To decide a class, you compare y to a threshold (often 0.5). The central formula in logistic regression is the logistic (sigmoid) function, shown below.

Where z is the linear combination of features x1 w1 + x2 w2 + ... + b, and sigma(z) is the predicted probability of the positive class. If sigma(z) >= 0.5, the label is 1; otherwise, it is 0. You can shift this threshold depending on class-imbalance or cost-sensitivity.

How would you evaluate the decision to convert one problem type into another in a production system?

You consider:

• Business Use Case: If you must give discrete labels for a pipeline that expects categorical outcomes, classification might be more pragmatic.

• Interpretability: Discrete predictions can be easier to interpret, but some tasks might benefit from the granularity of regression.

• Data Distribution: If your data naturally spans a range, forcing discrete bins could mask important trends.

• Performance: Check typical classification metrics (precision, recall, F1) versus regression metrics (RMSE, MAE). Conversions often require custom evaluation to make sense of the new labels.

Decisions often hinge on domain constraints, stakeholder needs, and the performance trade-off between discrete and continuous predictions.

Below are additional follow-up questions

Are there situations where a regression-based approach could outperform a pure classification model for a categorical problem?

One potential scenario is if there is a meaningful ordering or natural distance measure among the classes. Standard classification treats each label as an independent category, whereas a regression-based solution might leverage the ordered structure in the labels to capture the “distance” between classes. For example, in rating systems that use numeric scores (1, 2, 3, 4, 5), it may be beneficial to let a model predict a continuous score and then round it to the nearest integer to determine the final category. This can more smoothly capture how a rating of 4 is “closer” to 5 than to 1, whereas a typical multi-class classifier does not inherently model that distance.

However, a regression approach can introduce pitfalls. If the categories are purely nominal (like “red,” “blue,” “green”), forcing a numeric ordering is inappropriate. The network might learn incorrect assumptions about the “distance” between categories (e.g., the step from red to blue might not have the same meaning as from blue to green). In that situation, you would lose the correct notion of distinct categories and potentially damage performance.

How do missing or noisy labels affect the process of converting from regression to classification or vice versa?

When converting regression to classification through binning, missing values create extra complications because it’s unclear which bin they should belong to. Similarly, noisy continuous labels (e.g., incorrectly recorded measurements) might get assigned to a bin that does not reflect the true underlying category. This can degrade the quality of training data. Handling this often requires robust data cleaning, outlier detection, or imputation before binning.

For classification problems converted to regression, missing labels are similarly problematic because you cannot properly assign a numeric value if you do not know the correct class. If you have a small portion of missing labels, you might remove those samples or apply imputation strategies based on the mode or distribution of other categories. In practice, you must ensure that any data cleaning or imputation respects both the numeric representation and the underlying categorical meaning.

How should you address highly imbalanced bins when you convert a regression task into multiple classification bins?

When binning a continuous variable into categories (e.g., “low,” “medium,” “high”), it’s common to encounter skewed distributions. For instance, you might end up with 90% “low” and 10% “medium” and 0% “high.” Imbalanced data can lead classification models to bias heavily toward the majority class. Common strategies to address this:

• Choose quantile-based bins so each bin has roughly the same number of samples. This avoids some bins being nearly empty.

• Oversample minority bins or undersample the majority bin. Random oversampling or SMOTE-like algorithms for continuous data binned into categories can help.

• Use class-weighting in the loss function so that minority classes have higher cost for misclassification.

However, each approach can introduce trade-offs. Quantile-based bins might cause slightly unnatural category boundaries if your domain has clear threshold cutoffs. Oversampling can lead to overfitting to particular observations in the minority class. Adjusting class weights might make training more stable but still be sensitive to how the model generalizes.

If you convert a regression problem to classification and then use a neural network, how does the final layer and loss function differ compared to the regression-based architecture?

In a regression architecture, the final layer is typically a single linear neuron with no non-linear activation, and you optimize a regression loss such as mean squared error or mean absolute error. The network outputs a continuous value representing the predicted numerical target.

When converting to classification, the final layer architecture changes. If you are doing binary classification, you would typically have one output neuron with a sigmoid activation. You would optimize a loss function such as binary cross-entropy. For multi-class classification, you often have multiple output neurons with a softmax activation at the final layer, and you optimize a cross-entropy loss. Thus, the difference is primarily in the last layer (sigmoid/softmax) and the choice of a classification loss rather than a regression loss.

What are potential adverse consequences of applying ordinal regression techniques to classes that are truly nominal?

Ordinal regression assumes an inherent ordering among the categories (like “small,” “medium,” and “large”). But some classification problems have nominal classes, meaning there is no natural ordering among them (e.g., “dog,” “cat,” “rabbit”). If you treat these nominal classes with an ordinal method, the model will assume that “dog” < “cat” < “rabbit” (or some other numeric assignment), implying a sequence where none actually exists. This can distort relationships, mislead the learning algorithm, and degrade performance because the model tries to learn a numeric structure that does not fit the data. You would see side effects like unusual errors in predictions for classes that the model perceived as “far apart” or “close” despite no real similarity.

Is it possible or beneficial to combine both regression and classification outputs into a single model?

There are multitask learning scenarios where a single architecture might output a continuous metric and a categorical label simultaneously. For example, in healthcare, a model might predict a continuous risk score for a disease (regression) while also predicting whether the patient should be flagged for a particular treatment (binary classification). If these tasks share underlying features, a multitask learning setup can help the model learn better representations, leading to improved performance on both tasks.

However, this approach adds complexity. You must ensure the tasks are truly related and that optimizing for one does not negatively affect performance on the other. You also need to use loss functions that balance the separate objectives (e.g., a weighted sum of cross-entropy for classification and mean squared error for regression). Properly tuning these weights requires careful experimentation.

How can one convert classification output probabilities into a continuous score beyond a typical [0,1] range?

A standard classification model typically outputs a probability between 0 and 1 for each class (in binary classification, a single probability for the positive class). If the application needs a continuous output beyond that range, you can apply transformations post hoc. For instance, you could apply a log-odds transformation to “stretch” probabilities out of the [0,1] interval:

p in [0,1] can be converted to log(p/(1-p)) which can span (-∞, +∞). This yields a continuous score reflecting how strong the model’s belief is that the example belongs to the positive class. However, you must be careful with probabilities exactly 0 or 1 (the log-odds approach will be undefined for p=0 or p=1). In real applications, predicted probabilities rarely reach exactly 0 or 1, but if they do, you might cap them at 1e-5 or 1 - 1e-5 to avoid numerical errors.

When repurposing a classification model as a regression one, how do you interpret feature importance or coefficients?

In a classification context (like logistic regression), each coefficient indicates how a feature affects the log-odds of the positive class. In regression, a coefficient indicates how a feature affects the continuous numeric output. When you directly convert a classification label to a numeric label (e.g., class 0, 1, 2 mapped to 0.0, 1.0, 2.0), the interpretation of regression coefficients becomes linked to how a one-unit shift in that feature corresponds to a change in the numerical scale of classes. This can be misleading if the numeric coding is arbitrary or does not represent a genuine ranking.

For random forest or gradient-boosted models, feature importance metrics (like Gini importance for classification or variance reduction for regression) might still be used in principle. But the meaning of “importance” shifts with the learning objective. For classification, importance stems from how often the feature splits reduce classification impurity, while for regression, it stems from how much the feature splits reduce variance in the numeric target. If the numeric target is just an encoded class label, those splits might not align well with the original concept of categorical distinction.

How do you handle class labels that have no ordinal relationship when you force them into a regression framework?

If you cannot impose a meaningful ordering, any numeric mapping is arbitrary (e.g., dog -> 0, cat -> 1, rabbit -> 2). The regression model will implicitly assume that (cat - dog) has a numeric difference of 1 and (rabbit - cat) is also 1, which might not align with real relationships. To deal with that, you must accept that the numeric scale is an artificial construct. If the classes are purely nominal, you often lose performance or interpretability by doing regression. In practice, you should only do this if there is a compelling reason (e.g., your production pipeline accepts only continuous outputs, or you are exploring a learned ordering in your data). Otherwise, standard classification approaches are typically more suitable.

Does hyperparameter tuning differ between regression-based transformations and classification-based methods?

Yes, the choice of hyperparameters often depends on the loss function and metric you are optimizing. When converting to classification:

• You tune hyperparameters for cross-entropy loss or another classification-specific metric like F1 or AUC.

• Decision thresholds or class weights may be additional hyperparameters to optimize.

When converting to regression:

• You tune hyperparameters for mean squared error or mean absolute error.

• If you impose numeric labels on classes, you might need to consider how the numeric range and distribution affect regularization or learning rate.

Furthermore, techniques like early stopping or certain regularization strategies might behave differently depending on whether the objective is classification vs. regression. You should also carefully monitor overfitting because a model that does well at predicting numeric labels might perform poorly when those labels are a proxy for classes and not a true continuous variable.