Skip to main content

Uncertainty in Multiclass Classification

Dr. Rishabh Pathak
1. What is Uncertainty in Classification? Uncertainty refers to the model’s confidence or doubt in its predictions. Quantifying uncertainty is important to understand how reliable each prediction is. In multiclass classification , uncertainty estimates provide probabilities over multiple classes, reflecting how sure the model is about each possible class. 2. Methods to Estimate Uncertainty in Multiclass Classification Most multiclass classifiers provide methods such as: predict_proba: Returns a probability distribution across all classes. decision_function: Returns scores or margins for each class (sometimes called raw or uncalibrated confidence scores). The probability distribution from predict_proba captures the uncertainty by assigning a probability to each class. 3. Shape and Interpretation of predict_proba in Multiclass Output shape: (n_samples, n_classes) Each row corresponds to the probabilities of ...
Post a Comment

Uncertainty Estimates from Classifiers

Image
Dr. Rishabh Pathak

1. Overview of Uncertainty Estimates

  • Many classifiers do more than just output a predicted class label; they also provide a measure of confidence or uncertainty in their predictions.
  • These uncertainty estimates help understand how sure the model is about its decision, which is crucial in real-world applications where different types of errors have different consequences (e.g., medical diagnosis).

2. Why Uncertainty Matters

  • Predictions are often thresholded to produce class labels, but this process discards the underlying probability or decision value.
  • Knowing how confident a classifier is can:
  • Improve decision-making by allowing deferral in uncertain cases.
  • Aid in calibrating models.
  • Help in evaluating the risk associated with predictions.
  • Example: In medical testing, a false negative (missing a disease) can be worse than a false positive (extra test).

3. Methods to Obtain Uncertainty from Classifiers

3.1 decision_function

  • Some classifiers provide a decision_function method.
  • It outputs raw continuous scores (e.g., distances from the decision boundary in SVMs).
  • Thresholding this score produces a class prediction.
  • The value’s magnitude indicates confidence in the prediction.
  • Threshold is usually set at 0 for binary classification.

3.2 predict_proba

  • Most classifiers provide predict_proba method.
  • Outputs probabilities for each class.
  • Probabilities are values between 0 and 1, summing to 1 for all classes.
  • Thresholding these probabilities (e.g., > 0.5 in binary) produces predictions.
  • Probabilities provide an intuitive way to assess uncertainty.

4. Application in Binary and Multiclass Classification

  • Both decision_function and predict_proba work in binary and multiclass classification.
  • In multiclass settings, predict_proba gives a probability distribution over all classes, indicating the uncertainty in class membership.
  • This allows more nuanced interpretation than just picking the max probability.

5. Examples from scikit-learn

  • scikit-learn classifiers commonly have decision_function or predict_proba.
  • Important to note: Different classifiers produce different types of scores and probabilities.
  • Example:
  • Logistic regression outputs well-calibrated probabilities.
  • SVM decision_function outputs margin distances, which can be turned into probabilities using methods like Platt scaling.
  • scikit-learn allows assessing these uncertainty estimates easily, which can aid model evaluation and application decisions.

6. Effect on Model Evaluation

  • Standard metrics like accuracy or the confusion matrix collapse probabilistic outputs into hard decisions.
  • Using uncertainty estimates enables:
  • ROC curves (varying thresholds and observing tradeoffs).
  • Precision-recall curves.
  • Probability calibration curves.
  • These give a more detailed picture of model performance under uncertainty.

7. Limitations and Considerations

  • Not all classifiers produce well-calibrated uncertainty estimates.
  • Some models may be overconfident or underconfident.
  • Calibration techniques (e.g., Platt scaling, isotonic regression) can improve probability estimates.
  • Decision thresholds can be adjusted based on costs of different errors in the application domain.

8. Summary Table

Concept

Description

decision_function

Raw scores indicating distance from decision boundary

predict_proba

Probabilities for each class, summing to 1

Binary classification

Thresholding decision_function at 0 or predict_proba at 0.5

Multiclass classification

Probability distribution over classes for nuanced uncertainty

Real-world use

Helps decision-making where different errors have different costs

Model calibration

Necessary for reliable probability estimates

 

Categories:

Comments

Post a Comment

Popular posts from this blog

Relation of Model Complexity to Dataset Size

Dr. Rishabh Pathak
Core Concept The relationship between model complexity and dataset size is fundamental in supervised learning, affecting how well a model can learn and generalize. Model complexity refers to the capacity or flexibility of the model to fit a wide variety of functions. Dataset size refers to the number and diversity of training samples available for learning. Key Points 1. Larger Datasets Allow for More Complex Models When your dataset contains more varied data points , you can afford to use more complex models without overfitting. More data points mean more information and variety, enabling the model to learn detailed patterns without fitting noise. Quote from the book: "Relation of Model Complexity to Dataset Size. It’s important to note that model complexity is intimately tied to the variation of inputs contained in your training dataset: the larger variety of data points your dataset contains, the more complex a model you can use without overfitting....
Post a Comment
Read more

Linear Models

Dr. Rishabh Pathak
1. What are Linear Models? Linear models are a class of models that make predictions using a linear function of the input features. The prediction is computed as a weighted sum of the input features plus a bias term. They have been extensively studied over more than a century and remain widely used due to their simplicity, interpretability, and effectiveness in many scenarios. 2. Mathematical Formulation For regression , the general form of a linear model's prediction is: y^ ​ = w0 ​ x0 ​ + w1 ​ x1 ​ + … + wp ​ xp ​ + b where; y^ ​ is the predicted output, xi ​ is the i-th input feature, wi ​ is the learned weight coefficient for feature xi ​ , b is the intercept (bias term), p is the number of features. In vector form: y^ ​ = wTx + b where w = ( w0 ​ , w1 ​ , ... , wp ​ ) and x = ( x0 ​ , x1 ​ , ... , xp ​ ) . 3. Interpretation and Intuition The prediction is a linear combination of features — each feature contributes prop...
Post a Comment
Read more

Predicting Probabilities

Dr. Rishabh Pathak
1. What is Predicting Probabilities? The predict_proba method estimates the probability that a given input belongs to each class. It returns values in the range [0, 1] , representing the model's confidence as probabilities. The sum of predicted probabilities across all classes for a sample is always 1 (i.e., they form a valid probability distribution). 2. Output Shape of predict_proba For binary classification , the shape of the output is (n_samples, 2) : Column 0: Probability of the sample belonging to the negative class. Column 1: Probability of the sample belonging to the positive class. For multiclass classification , the shape is (n_samples, n_classes) , with each column corresponding to the probability of the sample belonging to that class. 3. Interpretation of predict_proba Output The probability reflects how confidently the model believes a data point belongs to each class. For example, in ...
Post a Comment
Read more

Kernelized Support Vector Machines

Dr. Rishabh Pathak
1. Introduction to SVMs Support Vector Machines (SVMs) are supervised learning algorithms primarily used for classification (and regression with SVR). They aim to find the optimal separating hyperplane that maximizes the margin between classes for linearly separable data. Basic (linear) SVMs operate in the original feature space, producing linear decision boundaries. 2. Limitations of Linear SVMs Linear SVMs have limited flexibility as their decision boundaries are hyperplanes. Many real-world problems require more complex, non-linear decision boundaries that linear SVM cannot provide. 3. Kernel Trick: Overcoming Non-linearity To allow non-linear decision boundaries, SVMs exploit the kernel trick . The kernel trick implicitly maps input data into a higher-dimensional feature space where linear separation might be possible, without explicitly performing the costly mapping . How the Kernel Trick Works: Instead of computing ...
Post a Comment
Read more

Supervised Learning

Dr. Rishabh Pathak
What is Supervised Learning? ·     Definition: Supervised learning involves training a model on a labeled dataset, where the input data (features) are paired with the correct output (labels). The model learns to map inputs to outputs and can predict labels for unseen input data. ·     Goal: To learn a function that generalizes well from training data to accurately predict labels for new data. ·          Types: ·          Classification: Predicting categorical labels (e.g., classifying iris flowers into species). ·          Regression: Predicting continuous values (e.g., predicting house prices). Key Concepts: ·     Generalization: The ability of a model to perform well on previously unseen data, not just the training data. ·         Overfitting and Underfitting: ·    ...
Post a Comment
Read more