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

At Gestational week 7 the cortical plate begins to develop

Image
Dr. Rishabh Pathak

At gestational week 7, a critical phase in brain development commences as the cortical plate begins to develop. Here is an explanation of the significance of gestational week 7 in the context of cortical plate development:


1.  Initiation of Cortical Plate Formation: Around gestational week 7, radially migrating neurons originating from the ventricular and subventricular zones initiate the development of the cortical plate. The cortical plate is a crucial structure in the developing brain that gives rise to the six distinct layers of the neocortex, the outer layer of the cerebral hemispheres responsible for higher cognitive functions.


2.     Early Cortical Layering: During the initial stages of cortical plate development, the structure is divided into two primary layers: the thin superficial marginal zone and the underlying subplate. The marginal zone contains cells that have migrated tangentially, while the subplate houses a mix of interneurons and post migratory pyramidal neurons. These early layers play essential roles in guiding the subsequent formation of the cortical layers.


3.     Inside-Out Formation of the Cortex: The cortical plate undergoes an inside-out formation process, where cortical neurons accumulate in a sequential manner. The earliest-born neurons destined to become the innermost layer 6 are followed by neurons that will form the outer layer 2. This inside-out sequence of neuronal migration and layer formation is crucial for establishing the laminar organization of the neocortex, which is essential for its functional specialization.


4.     Role of Radial Glial Cells: Radial glial cells, a type of neural stem cell that serves as a scaffold for neuronal migration, play a pivotal role in guiding the movement of neurons from the proliferative zones to their final destinations in the cortical plate. These cells provide structural support and guidance cues for migrating neurons, ensuring the proper positioning of neurons within the developing cortex.


5. Formation of Cortical Layers: The cortical plate development process ultimately leads to the formation of the six distinct layers of the neocortex. Each cortical layer contains specific types of neurons and plays unique roles in information processing and neural circuitry. The establishment of these layers is critical for the functional organization of the cerebral cortex and the development of complex cognitive abilities.


In summary, gestational week 7 marks a crucial stage in brain development when the cortical plate begins to form, setting the foundation for the intricate structure of the neocortex. The early events during cortical plate development, including neuronal migration, layering, and the inside-out formation of the cortex, are essential for establishing the laminar organization and functional specialization of the developing brain. Understanding the processes that unfold during cortical plate development is key to unraveling the complexities of brain development and the emergence of higher cognitive functions in the mature 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