Math and Architectures of Deep Learning

Probability distributions allow us to model uncertainty, analyze high-dimensional data, and form the basis for clustering, recommendation systems, and generative models. [1] [2]

PCA identifies the directions of maximum variance in data, enabling dimensionality reduction and noise elimination while preserving the underlying patterns. [1] [2]

LSA uses topic modeling by projecting document vectors onto topic axes, revealing latent similarities between documents that may not share explicit terms. [1]

Bayesian tools incorporate prior knowledge and uncertainty, enabling robust parameter estimation through concepts like conditional probability, entropy, and maximum likelihood. [1] [2]

Convolutions extract spatial features from data, forming the backbone of image, video, and signal processing in deep learning models. [1] [2]

Training involves computing outputs via forward propagation, then minimizing loss by updating weights through backpropagation and gradient descent. [1] [2]

CNNs leverage hierarchical feature extraction and deep architectures to achieve state-of-the-art performance in vision tasks like classification and detection. [1] [2]

Generative models learn compact latent representations that enable data generation, noise elimination, and streamlined data encoding. [1] [2]

ELBO provides a tractable objective for training VAEs by approximating the true posterior and minimizing KL divergence between distributions. [1]

Neural networks can learn mappings between complex data manifolds, offering a geometric perspective on how deep learning models transform data. [1] [2]