Skip to main content

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

Basic Model of Human Connectome Project

Image
Dr. Rishabh Pathak


 The Human Connectome Project (HCP) employs a comprehensive and multi-modal approach to map the structural and functional connectivity of the human brain. The basic model of the HCP involves the following key components:

  1. Data Acquisition:
    • The HCP collects neuroimaging data from a large cohort of healthy individuals using state-of-the-art imaging techniques.
    • Structural MRI: High-resolution structural MRI scans are acquired to visualize the anatomical features of the brain, such as gray matter, white matter, and cortical thickness.
    • Diffusion MRI: Diffusion MRI is used to map the white matter pathways in the brain by tracking the diffusion of water molecules along axonal fibers.
    • Functional MRI: Resting-state fMRI and task-based fMRI are employed to study the functional connectivity and activity patterns of the brain at rest and during specific cognitive tasks.
  2. Data Processing and Analysis:
    • The acquired neuroimaging data undergoes extensive processing and analysis to extract meaningful information about brain connectivity.
    • Structural Connectivity Analysis: Diffusion MRI data is processed to reconstruct white matter tracts and create maps of structural connectivity in the brain.
    • Functional Connectivity Analysis: Resting-state fMRI data is used to identify functional networks and correlations between different brain regions, providing insights into how the brain's functional networks are organized.
  3. Integration of Data:
    • The HCP integrates data from multiple imaging modalities, including structural MRI, diffusion MRI, and functional MRI, to create a comprehensive model of the human connectome.
    • By combining information from different imaging techniques, researchers can study the relationships between brain structure, function, and connectivity in a holistic manner.
  4. Connectome Mapping:
    • The primary goal of the HCP is to map the human connectome, which refers to the complete set of neural connections in the brain.
    • This mapping includes identifying structural connections (anatomical pathways) and functional connections (synchronized activity) between different brain regions.
    • The connectome maps generated by the HCP provide a detailed understanding of how information is processed and transmitted within the brain's network.
  5. Open Science and Data Sharing:
    • A fundamental principle of the HCP is open science and data sharing, where the generated datasets and connectome maps are made freely available to the scientific community.
    • This open access approach allows researchers worldwide to explore the rich neuroimaging data and contribute to advancing our understanding of the human brain.

Overall, the basic model of the Human Connectome Project involves acquiring, processing, and integrating neuroimaging data to create detailed maps of the human connectome, with a focus on structural and functional connectivity in the brain.

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

Kernelized Support Vector Machines

Dr. Rishabh Pathak
1. Introduction to SVMs Support Vector Machines (SVMs) are supervised learning algorithms primarily used for classification (and regression with SVR). They aim to find the optimal separating hyperplane that maximizes the margin between classes for linearly separable data. Basic (linear) SVMs operate in the original feature space, producing linear decision boundaries. 2. Limitations of Linear SVMs Linear SVMs have limited flexibility as their decision boundaries are hyperplanes. Many real-world problems require more complex, non-linear decision boundaries that linear SVM cannot provide. 3. Kernel Trick: Overcoming Non-linearity To allow non-linear decision boundaries, SVMs exploit the kernel trick . The kernel trick implicitly maps input data into a higher-dimensional feature space where linear separation might be possible, without explicitly performing the costly mapping . How the Kernel Trick Works: Instead of computing ...
Post a Comment
Read more

Supervised Learning

Dr. Rishabh Pathak
What is Supervised Learning? ·     Definition: Supervised learning involves training a model on a labeled dataset, where the input data (features) are paired with the correct output (labels). The model learns to map inputs to outputs and can predict labels for unseen input data. ·     Goal: To learn a function that generalizes well from training data to accurately predict labels for new data. ·          Types: ·          Classification: Predicting categorical labels (e.g., classifying iris flowers into species). ·          Regression: Predicting continuous values (e.g., predicting house prices). Key Concepts: ·     Generalization: The ability of a model to perform well on previously unseen data, not just the training data. ·         Overfitting and Underfitting: ·    ...
Post a Comment
Read more