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

Non-probability Sampling

Image
Dr. Rishabh Pathak

Non-probability sampling is a sampling technique where the selection of sample units is based on the judgment of the researcher rather than random selection. In non-probability sampling, each element in the population does not have a known or equal chance of being included in the sample. Here are some key points about non-probability sampling:


1.    Definition:

o   Non-probability sampling is a sampling method where the selection of sample units is not based on randomization or known probabilities.

o    Researchers use their judgment or convenience to select sample units that they believe are representative of the population.

2.    Characteristics:

o    Non-probability sampling methods do not allow for the calculation of sampling error or the generalizability of results to the population.

o  Sample units are selected based on the researcher's subjective criteria, convenience, or accessibility.

3.    Types of Non-probability Sampling:

o    Convenience Sampling: Sample units are selected based on their availability and accessibility to the researcher. This method is convenient but may introduce bias.

o    Purposive Sampling: Sample units are selected based on specific criteria determined by the researcher's judgment. This method is used when specific characteristics are of interest.

o  Snowball Sampling: Existing participants in the study help identify and recruit additional participants. This method is useful for hard-to-reach populations.

o    Quota Sampling: Sample units are selected to meet predetermined quotas based on certain characteristics. This method is used to ensure representation of specific subgroups.

4.    Advantages:

o    Non-probability sampling methods are often quicker, easier, and more cost-effective than probability sampling methods.

o  These methods can be useful when studying rare populations, conducting exploratory research, or when random sampling is not feasible.

5.    Limitations:

o Results obtained from non-probability sampling may not be generalizable to the larger population due to selection bias.

o    The lack of randomization in non-probability sampling can lead to sampling errors and reduced external validity.

o    Researchers need to be cautious in interpreting and generalizing findings from non-probability samples.

6.    Applications:

o  Non-probability sampling is commonly used in qualitative research, pilot studies, case studies, and exploratory research where the focus is on understanding specific phenomena rather than making population inferences.

Non-probability sampling methods play a valuable role in research, particularly in exploratory studies or when random sampling is not feasible. While these methods offer flexibility and convenience, researchers should be aware of their limitations in terms of generalizability and potential bias in sample selection. Careful consideration of the research objectives and population characteristics is essential when choosing non-probability sampling methods.

 

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 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

Classification and Regression

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 (less commonly covered in this book). Key Concepts: The class labels are discrete and come from a finite set . Often expressed as a yes/no question in binary classifi...
Post a Comment
Read more