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

Simple Random Sampling Without Replacement

Image
Dr. Rishabh Pathak

Simple random sampling without replacement is a fundamental sampling technique used in research to select a subset of items from a larger population in such a way that each item has an equal probability of being chosen, and once an item is selected, it is not replaced back into the population. Here is an overview of how simple random sampling without replacement works:


1.    Population and Sampling Frame:

§  The population refers to the entire group of interest from which the sample will be drawn. A sampling frame is a list or representation of all the elements in the population that are accessible for sampling.

2.    Assigning Numbers:

§  Each element in the population is assigned a unique identifier or number. These numbers are used to distinguish and select individual items during the sampling process.

3.    Random Selection:

§  To conduct simple random sampling without replacement, researchers use a random selection method to choose items from the population. This can be done using random number tables, software, or other randomization techniques.

4.    Selection Process:

§  Researchers start by selecting a random starting point in the sampling frame. They then proceed to select items systematically based on a random pattern, ensuring that each item has an equal chance of being chosen.

5.    Sample Size:

§  The sample size is predetermined based on the research objectives and statistical considerations. In simple random sampling without replacement, each selected item reduces the pool of available items for subsequent selections.

6.    Representativeness:

§  By ensuring that each item in the population has an equal probability of being included in the sample, simple random sampling without replacement helps in creating a representative sample that reflects the characteristics of the larger population.

7.    Statistical Analysis:

§  Once the sample is selected, researchers can analyze the sample data using various statistical methods to draw conclusions and make inferences about the population. The results obtained from the sample can be generalized to the population with appropriate statistical techniques.

8.    Advantages:

§  Simple random sampling without replacement is straightforward, easy to understand, and helps in reducing bias in the sample selection process. It provides a basis for statistical inference and allows researchers to estimate population parameters with known precision.

9.    Limitations:

§  One limitation of simple random sampling without replacement is that it may not be practical for very large populations, as the process of selecting samples without replacement can become cumbersome. In such cases, other sampling methods like stratified sampling or cluster sampling may be more efficient.

Simple random sampling without replacement is a foundational sampling method that forms the basis for many other sampling techniques. By following the principles of randomness and equal probability, researchers can ensure the validity and reliability of their research findings when using this sampling approach.

 

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

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

Ensembles of Decision Trees

Dr. Rishabh Pathak
1. What are Ensembles? Ensemble methods combine multiple machine learning models to create more powerful and robust models. By aggregating the predictions of many models, ensembles typically achieve better generalization performance than any single model. In the context of decision trees, ensembles combine multiple trees to overcome limitations of single trees such as overfitting and instability. 2. Why Ensemble Decision Trees? Single decision trees: Are easy to interpret but tend to overfit training data, leading to poor generalization,. Can be unstable because small variations in data can change the structure of the tree significantly. Ensemble methods exploit the idea that many weak learners (trees that individually overfit or only capture partial patterns) can be combined to form a strong learner by reducing variance and sometimes bias. 3. Two Main Types of Tree Ensembles (a) Random Forests Random forests are ensembles con...
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