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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...
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Generalization, Overfitting and Underfitting

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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.

 

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