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

Supervised Learning

Image
Dr. Rishabh Pathak

Supervised learning is a fundamental approach in machine learning where models are trained on a labeled dataset. This method involves providing the algorithm with input-output pairs so that it can learn to map inputs to their respective outputs.

1. Definition of Supervised Learning

Supervised learning is a machine learning paradigm where the model is trained on a dataset containing input-output pairs. The goal is to learn a function that, given an input, produces the correct corresponding output. This process involves using a labeled dataset, where each input data point is associated with a known output (response variable).

2. Components of Supervised Learning

  • Input Features (X): The independent variables or characteristics used to predict the output.
  • Output (Y): The dependent variable or target that the model aims to predict.
  • Training Set: A collection of labeled examples used to fit the model, typically represented as pairs (x(i),y(i)) where i indexes each example.
  • Model: A mathematical description of the relationship between input data and output predictions.

3. Types of Supervised Learning

Supervised learning can be broadly divided into two main categories:

  • Classification: The task of predicting a discrete label (class) for given input data. Examples include:
  • Binary Classification: Two possible classes (e.g., spam vs. non-spam emails).
  • Multi-class Classification: More than two classes (e.g., classifying types of animals).
  • Regression: The task of predicting a continuous output variable based on input features. Examples include:
  • Predicting housing prices based on features like square footage and number of bedrooms.
  • Forecasting stock prices based on historical data.

4. Common Algorithms in Supervised Learning

Several algorithms are commonly used in supervised learning, each with its strengths and weaknesses:

  • Linear Regression: Used for regression tasks; models the relationship between input features and the continuous output as a linear function.
  • Logistic Regression: A statistical model used for binary classification; models the probability that a given input belongs to a particular class using a logistic function.
  • Decision Trees: A tree-like model that makes decisions based on the values of input features, partitioning the dataset into branches that represent possible outcomes.
  • Support Vector Machines (SVM): Classifiers that find the optimal hyperplane that maximizes the margin between different classes.
  • K-Nearest Neighbors (KNN): A non-parametric method where predictions are made based on the 'k' closest training examples in the feature space.
  • Neural Networks: Computational models inspired by the human brain, particularly effective for both classification and regression tasks, especially with large datasets and complex relationships.

5. Training Process

The training process in supervised learning involves the following steps:

1.    Data Collection: Gather a sufficiently large and representative dataset comprising input-output pairs.

2.  Data Preparation: Clean and preprocess data, including handling missing values, normalization, and encoding categorical variables.

3. Model Selection: Choose an appropriate algorithm and model architecture based on the problem at hand.

4.  Training: Fit the model to the training data by adjusting model parameters to minimize the error between predicted outputs and actual outputs. This involves:

  • Dividing the dataset into training and testing (or validation) sets.
  • Utilizing a loss function to gauge how well the model performs on the training set.

5.     Testing and Validation: Evaluate the model's performance on unseen data to check how well it generalizes. Common practices include cross-validation.

6. Evaluation Metrics

To assess the performance of a supervised learning model, several metrics can be employed, including:

  • Accuracy: The proportion of correct predictions over the total predictions (used mainly in classification tasks).
  • Precision: The ratio of true positive predictions to the total predicted positives (important in imbalanced datasets).
  • Recall (Sensitivity): The ratio of true positives to the total actual positives (also relevant for imbalanced classes).
  • F1 Score: The harmonic mean of precision and recall, serving as a balance between the two metrics.
  • Mean Squared Error (MSE): Used for regression, it measures the average squared difference between the predicted and actual values.

7. Applications of Supervised Learning

Supervised learning has extensive applications across various fields:

  • Healthcare: Diagnosing diseases and predicting patient outcomes based on historical health records.
  • Finance: Risk assessment and credit scoring.
  • Marketing: Predicting customer behavior and segmenting customers based on purchase history.
  • Image Recognition: Classifying images into categories, such as identifying objects or persons in pictures.
  • Speech Recognition: Translating spoken language into text, useful in virtual assistants.

8. Conclusion

Supervised learning is a powerful and widely used approach in machine learning that provides a structured way to learn from labeled datasets. By understanding its components, various algorithms, and evaluation methods, practitioners can build models that effectively solve real-world problems.

For further details, most concepts regarding supervised learning are discussed in your lecture notes, particularly in the sections focusing on linear regression and classification problems.

 

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