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QR-decomposition-solver-course

QR decomposition, or QR factorization, is a fundamental linear algebra method that decomposes a matrix into a product of an orthogonal matrix and an upper triangular matrix. It is widely used for solving linear least squares problems, computing eigenvalues, Gram-Schmidt, Householder reflections, or Givens rotations.Solver

stochastic-average-gradient-sag-solver-course

The SAG + Accelerated (Stochastic Average Gradient) solver is an optimization algorithm used primarily in machine learning, specifically for logistic regression and linear support vector machines (SVMs) within libraries like scikit-learn. It is designed to be highly efficient for large datasets with many samples and features. Solver

L2-regularization-ridge-regression-course

L2 regularization, or Ridge regression, is a technique to prevent overfitting in machine learning by adding a penalty proportional to the sum of squared weights to the loss function. It forces weights to be small but rarely zero, resulting in a smoother, more stable model. Solver

underfitting-overfitting-polynomial-regression-course

Underfitting and overfitting are critical concepts in machine learning, particularly when using Polynomial Regression to model data. Polynomial regression allows a model to learn non-linear relationships by increasing the polynomial degree (e.g. ), making it highly susceptible to both underfitting (too simple) and overfitting (too complex).Solver

LSQR-solver-course

LSQR is an iterative method for solving large, sparse, linear systems of equations and linear least-squares problems, including under- or over-determined and rank-deficient systems. It uses the Lanczos bidiagonalization process to provide a robust alternative to conjugate gradients, offering better numerical stability. Solver

conjugate-gradient-sparse-cg-solver-course

The Conjugate Gradient (CG) method is an efficient iterative algorithm for solving large, sparse systems of linear equations where the matrix is symmetric and positive-definite. It finds the minimum of a quadratic function by generating conjugate search directions, ensuring convergence in at most steps for an matrix.Solver

gradient-descent-sgd-solver-course

Stochastic Gradient Descent (SGD) is an optimization algorithm that updates model parameters iteratively using small, random subsets (batches) of data, rather than the entire dataset. It significantly speeds up training for large datasets, though it introduces noise that causes, in some cases, heavy fluctuations.deep learning/neural networks.solver

cholesky-decomposition-solver-course

Cholesky decomposition is a matrix factorization method that decomposes a symmetric, positive-definite matrix into the product of a lower triangular matrix and its transpose (i.e., ). LU decomposition for solving linear equations and is widely used in Monte Carlo simulations, Kalman filters, and econometrics. Solver

singular-value-decomposition-svd-solver-course

Singular Value Decomposition (SVD) is a fundamental linear algebra technique that factorizes any into the product of three matrices: are orthogonal matrices containing left and right singular vectors, while sigma is a diagonal matrix of non-negative singular values. It is essential for data reduction, noise removal, and matrix approximation.Solver

Normal-equation-solver-multiple-linear-regression-course

Multiple Linear Regression (MLR) models the linear relationship between a continuous dependent variable and two or more independent (explanatory) variables. Using the equation, it predicts outcomes based on multiple factors. Key assumptions include linearity, constant variance of residuals, and low correlation between independent variables.Solver