Skip to main content

Unveiling Hidden Neural Codes: SIMPL – A Scalable and Fast Approach for Optimizing Latent Variables and Tuning Curves in Neural Population Data

Dr. Rishabh Pathak
This research paper presents SIMPL (Scalable Iterative Maximization of Population-coded Latents), a novel, computationally efficient algorithm designed to refine the estimation of latent variables and tuning curves from neural population activity. Latent variables in neural data represent essential low-dimensional quantities encoding behavioral or cognitive states, which neuroscientists seek to identify to understand brain computations better. Background and Motivation Traditional approaches commonly assume the observed behavioral variable as the latent neural code. However, this assumption can lead to inaccuracies because neural activity sometimes encodes internal cognitive states differing subtly from observable behavior (e.g., anticipation, mental simulation). Existing latent variable models face challenges such as high computational cost, poor scalability to large datasets, limited expressiveness of tuning models, or difficulties interpreting complex neural network-based functio...
Post a Comment

Classification and Regression

Image
Dr. Rishabh Pathak


 Classification

Definition:

Classification is the supervised learning task of predicting a categorical class label from input data. Each example in the dataset belongs to one of a predefined set of classes.

Characteristics:

  • Outputs are discrete.
  • The goal is to assign each input to a single class.
  • Classes can be binary (two classes) or multiclass (more than two classes).

Examples:

  • Classifying emails as spam or not spam (binary classification).
  • Classifying iris flowers into one of three species (multiclass classification).

Types of Classification:

  • Binary Classification: Distinguishing between exactly two classes.
  • Multiclass Classification: Distinguishing among more than two classes.
  • Multilabel Classification: Assigning multiple class labels to each instance.

Key Concepts:

  • The class labels are discrete and come from a finite set.
  • Often expressed as a yes/no question in binary classification (e.g., “Is this email spam?”).
  • The predicted class labels are often encoded numerically but represent categories (e.g., 0, 1, 2 for iris species).

Regression

Definition:

Regression is the supervised learning task of predicting a continuous numerical value based on input features.

Characteristics:

  • Outputs are continuous and often real-valued numbers.
  • The model predicts a numeric quantity rather than a class.

Examples:

  • Predicting a person’s annual income from age, education, and location.
  • Predicting crop yield given weather and other factors.

Key Concepts:

  • Unlike classification, the output is a continuous value.
  • The task is about estimating the underlying function that maps inputs to continuous outputs.
  • Outputs can theoretically be any number within a range, reflecting real-world quantities.

Distinguishing Between Classification and Regression

An intuitive way to differentiate is based on the continuity of the output:

  • If the output is discrete (categorical classes), the problem is classification.
  • If the output is continuous (numerical values), the problem is regression.

Practical Examples and Representations:

  • The Iris dataset is a classic example for classification, with three species as classes.
  • For regression, datasets might involve predicting house prices, temperatures, or yields, with outputs as continuous numbers.
  • Input data can be numerical or categorical, but models require proper encoding and representation (e.g., one-hot encoding for categorical variables).

Summary and Usage

  • Classification and regression are foundational supervised learning tasks.
  • Choosing the right algorithm depends on the nature of the output (categorical vs continuous).
  • Preprocessing and feature representation are critical for both tasks to achieve good performance.
  • Many algorithms can be adapted for either task, but the interpretation and training differ accordingly.
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

Uncertainty Estimates from Classifiers

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 ...
Post a Comment
Read more

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
Read more