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

Generalization, Overfitting and Underfitting

Image
Dr. Rishabh Pathak

Generalization

Definition:

  • Generalization refers to a machine learning model's ability to perform well on new, unseen data that is drawn from the same distribution as the training data.
  • The core goal of supervised learning is to learn a model that generalizes from the training set to accurately predict outcomes for new data points.

Importance:

  • A model that generalizes well captures the underlying patterns in the data instead of memorizing training examples.
  • Without good generalization, a model may perform well on the training data but poorly on any new data, which is undesirable in real-world applications.

Overfitting

Definition:

  • Overfitting occurs when a model learns the noise and random fluctuations in the training data instead of the true underlying distribution.
  • The model fits the training data too closely, capturing minor details that do not generalize.

Characteristics:

  • Very low error on the training set.
  • Poor performance on new or test data.
  • Decision boundaries or predictions are overly complex and finely tuned to training points, including outliers.

Causes of Overfitting:

  • Model complexity is too high relative to the amount and noisiness of data.
  • Insufficient training data to support a complex model.
  • Lack of proper regularization or early stopping strategies.

Illustrative Example:

  • Decision trees with pure leaves classify every training example correctly, which corresponds to overfitting by fitting to noise and outliers (Figure 2-26 on page 88).
  • k-Nearest Neighbor with k=1 achieves perfect training accuracy but often poorly generalizes to new data.

Underfitting

Definition:

  • Underfitting occurs when a model is too simple to capture the underlying structure and patterns in the data.
  • The model performs poorly on both the training data and new data.

Characteristics:

  • High error on training data.
  • High error on test data.
  • Model predictions are overly simplified, missing important relationships.

Causes of Underfitting:

  • Model complexity is too low.
  • Insufficient features or lack of expressive power.
  • Too strong regularization preventing learning of meaningful patterns.

The Trade-Off Between Overfitting and Underfitting

Model Complexity vs. Dataset Size:

  • There is a balance or "sweet spot" to be found where the model is complex enough to explain the data but simple enough to avoid fitting noise.
  • The relationship between model complexity and performance typically forms a U-shaped curve.

Model Selection:

  • Effective supervised learning requires choosing a model with the right level of complexity.
  • Techniques include hyperparameter tuning (e.g., k in k-nearest neighbors), pruning in decision trees, regularization, and early stopping.

Impact of Scale and Feature Engineering:

  • Proper scaling and representation of input features significantly affect the model's ability to generalize and reduce overfitting or underfitting.

Strategies to Mitigate Overfitting and Underfitting

·         Mitigating Overfitting:

·         Use simpler models.

·         Apply regularization (L1/L2).

·         Early stopping in iterative algorithms.

·         Prune decision trees (post-pruning or pre-pruning).

·         Increase training data size.

·         Mitigating Underfitting:

·         Use more complex models.

·         Add more features or use feature engineering.

·         Reduce regularization.

Summary

Aspect

Overfitting

Underfitting

Model Complexity

Too high

Too low

Training Performance

Very good

Poor

Test Performance

Poor

Poor

Cause

Learning noise; focusing on outliers and noise

Oversimplification; lack of feature learning

Example

Deep decision trees, k-NN with k=1

Linear model on a nonlinear problem

The ultimate goal is to find a model that generalizes well by balancing these extremes.

 

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