Machine Learning: Generative and Discriminative Models

Multiclass Logistic Regression - University at Buffalo

Probabilistic Discriminative Models •Generative vsDiscriminative 1.Fixed basis functions in linear classification 2.Logistic Regression (two-class) 3.Iterative Reweighted Least Squares (IRLS) 4.Multiclass Logistic Regression 5.ProbitRegression 6.Canonical Link Functions 2 Machine Learning Srihari

  Model, Logistics, Regression, Logistic regression

Machine Learning Basics: Estimators, Bias and Variance

Machine Learning Basics: Estimators, Bias and Variance Sargur N. Srihari srihari@cedar.buffalo.edu ... • To distinguish estimates of parameters from their true value, a point estimate of a parameter θ is represented by • Let {x(1), x(2),..x(m)} be m independent and

  Machine, Parameters

The Hessian Matrix - University at Buffalo

Diagonal Approximation • In many case inverse of Hessian is needed • If Hessian is approximated by a diagonal matrix (i.e., off-diagonal elements are zero), its inverse is trivially computed • Complexity is O(W) rather than O(W2) for full Hessian 7

  Matrix, Diagonal, Diagonal matrix

Backpropagation - University at Buffalo

Machine Learning Srihari Matrix Multiplication: Forward Propagation •Each layer is a function of layer that preceded it •First layer is given by z =h(W(1)T x +b(1)) •Second layer is y = σ(W(2)T x +b(2)) •Note that W is a matrix rather than a vector

Machine Learning Basics: Supervised Learning Algorithms

Deep Learning Probabilistic Supervised Classification Srihari • If we only have two classes we only need to specify the distribution for one of these classes – The probability of the other class is known – Linear regression has a closed-form solution – But …

  Learning

Gaussian Distribution - Welcome to CEDAR

• For a multivariate Gaussian distribution N(x| µ,Λ-1) for a D-dimensional variable x – Conjugate prior for mean µ assuming known precision is Gaussian – For known mean and unknown precision matrix Λ, conjugate prior is Wishart distribution – If both mean and precision are unknown conjugate prior is Gaussian-Wishart

  Distribution, Multivariate, Gaussian, Gaussian distribution, Multivariate gaussian distributions

Gaussian Derivatives - University at Buffalo

• Slice the surface with horizontal planes which the locus of points with the quadratic form. INFORMATION THEORY. Relative Entropy. ... great generality, and it is useful when we seek to know whether something other than the assumed case …

  Panels, Great

Iterative Reweighted Least Squares

•Derivative has the form •Setting equal to zero and solving we get Machine Learning Srihari 4 y(x,w)=w j ... 3.Gradient 4.Hessian 5.Newton-Raphsonupdate …

  Derivatives

Chomsky's Generative Transformational ... - univ-eloued.dz

In Syntactic Structures (1957), Chomsky proposed three models for the structure of the language; the Finite Markov Process, Phrase Structure Model, which is based on immediate constituent analysis and Transformational Generative Grammar TGG. All in all, the aim of the linguistic theory expounded by Chomsky in Syntactic

  Model, Generative

Time-series Generative Adversarial Networks - NIPS

TimeGAN is a generative time-series model, trained adversarially and jointly via a learned embedding space with both supervised and unsupervised losses. As such, our approach straddles the intersection of multiple strands of research, combining themes from autoregressive models for sequence prediction,

  Model, Generative

GIRAFFE: Representing Scenes As Compositional Generative ...

generative models operate in 2D, we incorporate a compo-sitional 3D scene representation into the generative model. This leads to more consistent image synthesis results, e.g. note how, in contrast to our method, translating one object might change the other when operating in 2D (Fig. 2a and 2b). It further allows us to perform complex ...

  Model, Generative, Generative models

Latent Dirichlet Allocation - Home - Stanford Artificial ...

Latent Dirichlet allocation (LDA) is a generative probabilistic model of a corpus. The basic idea is that documents are represented as random mixtures over latent topics, where each topic is charac-terized by a distribution over words.1 LDA assumes the following generative process for each document w in a corpus D: 1. Choose N ˘Poisson(ξ). 2.

  Generative

Perceptual Generative Adversarial Networks for Small ...

2.2. Generative Adversarial Networks The Generative Adversarial Networks (GANs) [14]is a framework for learning generative models. Mathieu et al. [26] and Dentonet al. [6] adopted GANs for the appli-cation of image generation. In [22] and [40], GANs were employed to learn a mapping from one manifold to another

  Network, Model, Small, Adversarial, Generative, Perceptual, Generative models, Perceptual generative adversarial networks for small

Improving Language Understanding by Generative Pre …

discriminatively trained models to perform adequately. We demonstrate that large gains on these tasks can be realized by generative pre-training of a language model on a diverse corpus of unlabeled text, followed by discriminative fine-tuning on each specific task. In contrast to previous approaches, we make use of task-aware input

  Model, Understanding, Generative

Unsupervised Anomaly Detection with Generative Adversarial ...

GANs enable to learn generative models generating detailed realistic im-ages [9,10,11]. Radford et al. [12] introduced deep convolutional generative ad-versarial networks (DCGANs) and showed that GANs are capable of capturing semantic image content enabling vector arithmetic for visual concepts. Yeh et

  Model, Generative, Generative models

Jukebox: A Generative Model for Music - arXiv

The field of generative models has made tremendous progress in the last few years. One of the aims of gen-erative modeling is to capture the salient aspects of the data and to generate new instances indistinguishable from the true data The hypothesis is that by learning to produce the data we can learn the best features of the data1. We are

  Model, Generative, Evitare, Generative models, Gen erative