A Unifying review of linear gaussian models

Factor analysis, principal component analysis, mixtures of gaussian clusters, vector quantization, Kalman filter models, and hidden Markov models can all be unified as variations of unsupervised learning under a single basic generative model. This is achieved by collecting together disparate observations and derivations made by many previous authors and introducing a new way of linking discrete and continuous state models using a simple nonlinearity. Through the use of other nonlinearities, we show how independent component analysis is also a variation of the same basic generative model.We show that factor analysis and mixtures of gaussians can be implemented in autoencoder neural networks and learned using squared error plus the same regularization term. We introduce a new model for static data, known as sensible principal component analysis, as well as a novel concept of spatially adaptive observation noise. We also review some of the literature involving global and local mixtures of the basic models and provide pseudocode for inference and learning for all the basic models

Generalized Maximum Entropy estimation of discrete sequential move games of perfect information

We propose a data-constrained generalized maximum entropy (GME) estimator for discrete sequential move games of perfect information which can be easily implemented on optimization software with high-level interfaces such as GAMS. Unlike most other work on the estimation of complete information games, the method we proposed is data constrained and does not require simulation and normal distribution of random preference shocks. We formulate the GME estimation as a (convex) mixed-integer nonlinear optimization problem (MINLP) which is well developed over the last few years. The model is identified with only weak scale and location normalizations, monte carlo evidence demonstrates that the estimator can perform well in moderately size samples. As an application, we study the social security acceptance decisions in dual career households.Game-Theoretic Econometric Models, Sequential-Move Game, Generalized Maximum Entropy, Mixed-Integer Nonlinear Programming