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Operations Research, Systems Engineering and Industrial Engineering *Commons*^{™}

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Articles **1** - **3** of ** 3**

## Full-Text Articles in Operations Research, Systems Engineering and Industrial Engineering

Properties And Bayesian Fitting Of Restricted Boltzmann Machines, Andee Kaplan, Daniel J. Nordman, Stephen B. Vardeman

#### Properties And Bayesian Fitting Of Restricted Boltzmann Machines, Andee Kaplan, Daniel J. Nordman, Stephen B. Vardeman

*Statistics Preprints*

A restricted Boltzmann machine (RBM) is an undirected graphical model constructed for discrete or continuous random variables, with two layers, one hidden and one visible, and no conditional dependency within a layer. In recent years, RBMs have risen to prominence due to their connection to deep learning. By treating a hidden layer of one RBM as the visible layer in a second RBM, a deep architecture can be created. RBMs are thought to thereby have the ability to encode very complex and rich structures in data, making them attractive for supervised learning. However, the generative behavior of RBMs is largely ...

On The Instability And Degeneracy Of Deep Learning Models, Andee Kaplan, Daniel J. Nordman, Stephen B. Vardeman

#### On The Instability And Degeneracy Of Deep Learning Models, Andee Kaplan, Daniel J. Nordman, Stephen B. Vardeman

*Statistics Preprints*

A probability model exhibits instability if small changes in a data outcome result in large, and often unanticipated, changes in probability. This instability is a property of the probability model, rather than the fitted parameter vector. For correlated data structures found in several application areas, there is increasing interest in predicting/identifying such sensitivity in model probability structure. We consider the problem of quantifying instability for general probability models defined on sequences of observations, where each sequence of length N has a finite number of possible values. A sequence of probability models results, indexed by N, that accommodates data of ...

Alternating Direction Method Of Multipliers For Penalized Zero-Variance Discriminant Analysis, Brendan P.W. Ames, Mingyi Hong

#### Alternating Direction Method Of Multipliers For Penalized Zero-Variance Discriminant Analysis, Brendan P.W. Ames, Mingyi Hong

*Industrial and Manufacturing Systems Engineering Publications*

We consider the task of classification in the high dimensional setting where the number of features of the given data is significantly greater than the number of observations. To accomplish this task, we propose a heuristic, called sparse zero-variance discriminant analysis, for simultaneously performing linear discriminant analysis and feature selection on high dimensional data. This method combines classical zero-variance discriminant analysis, where discriminant vectors are identified in the null space of the sample within-class covariance matrix, with penalization applied to induce sparse structures in the resulting vectors. To approximately solve the resulting nonconvex problem, we develop a simple algorithm based ...