High Dimension Data

Logistic regression is a supervised machine learning algorithm used for binary classification tasks. Unlike linear regression, which predicts continuous values, logistic regression predicts the probability that a given input belongs to a certain class.

Linear Model Optimization

Regularization is a way to make sure our model doesn't become too complicated. It ensures the model doesn’t overfit the training data while still making good predictions on new data. Think of it as adding a 'rule' or 'constraint' that prevents the model from relying too much on any specific feature or predictor.

Softmax is a mathematical function commonly used in machine learning, particularly in the context of classification problems. It transforms a vector of raw scores, often called logits, from a model into a vector of probabilities that sum to one. The probabilities generated by the softmax function represent the likelihood of each class being the correct classification. $$\sigma(\mathbf{z})_i = \frac{e^{z_i}}{\sum_{j=1}^K e^{z_j}}$$

Support Vector Machine (SVM) is a supervised learning algorithm used for classification and regression. It finds the best hyperplane that separates the data into different classes with the largest possible margin. SVM can work well with high-dimensional data and use different kernel functions to transform data for better separation when it is not linearly separable.$$f(x) = sign(w^T x + b)$$

Random Forest is an ensemble machine learning algorithm that builds multiple decision trees during training and merges their outputs to improve accuracy and reduce overfitting. It is commonly used for both classification and regression tasks. By averaging the predictions of several decision trees, Random Forest reduces the variance and increases model robustness, making it less prone to errors from noisy data. $$\text{Entropy}_{\text{after}} = \frac{|S_l|}{|S|}\text{Entropy}(S_l) + \frac{|S_r|}{|S|}\text{Entropy}(S_r)$$

DLVO theory is named after Derjaguin, Landau, Verwey, and Overbeek, who developed it in the 1940s. It describes the forces between charged surfaces interacting through a liquid medium. The theory combines two main types of forces

The avian immune system exhibits a unique immunoglobulin (Ig) system characterized by distinct features absent in other vertebrates. Birds possess a specialized IgY, which serves as the functional equivalent to mammalian IgG and IgE, but with significant structural and functional differences. Unlike mammalian systems, birds utilize a limited number of germline gene segments and rely on gene conversion within the bursa of Fabricius to generate antibody diversity. This mechanism allows for a rapid and diverse immune response, showcasing the evolutionary adaptation of birds to their ecological niches and pathogen challenges.

The 12/23 rule is fundamental in the V(D)J recombination process, which assembles the variable (V), diversity (D), and joining (J) gene segments in the immune system to create diverse antibodies and T cell receptors. The rule stipulates that recombination can only occur between a gene segment flanked by a recombination signal sequence (RSS) with a 12-base pair (bp) spacer and one with a 23-bp spacer. This ensures proper alignment and prevents inappropriate recombination, thereby maintaining the integrity and functionality of the immune response​.

Multi-layer Neural Nets

Hidden Markov Model

Perceptron

Linear Regression

Learning Progress