Tractable Multivariate Binary Density Estimation and the Restricted Boltzmann Forest

We investigate the problem of estimating the density function of multivariate binary data. In particular, we focus on models for which computing the estimated probability of any data point is tractable. In such a setting, previous work has mostly concentrated on mixture modeling approaches. We argue that for the problem of tractable density estimation, the restricted Boltzmann machine (RBM) provides a competitive framework for multivariate binary density modeling. With this in mind, we also generalize the RBM framework and present the restricted Boltzmann forest (RBForest), which replaces the binary variables in the hidden layer of RBMs with groups of tree-structured binary variables. This extension allows us to obtain models that have more modeling capacity but remain tractable. In experiments on several data sets, we demonstrate the competitiveness of this approach and study some of its properties.

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Mixture Models Based on Neural Network Averaging

Neural Computation ◽

10.1162/089976606774841576 ◽

2006 ◽

Vol 18 (1) ◽

pp. 1-9 ◽

Cited By ~ 5

Author(s):

Walter W. Focke

Keyword(s):

Neural Network ◽

Transfer Function ◽

Mixture Model ◽

Network Architecture ◽

Binary Data ◽

Data Sets ◽

Wilson Equation ◽

Power Mean ◽

Hidden Layer ◽

Box Cox Transformation

A modified version of the single hidden-layer perceptron architecture is proposed for modeling mixtures. A particular flexible mixture model is obtained by implementing the Box-Cox transformation as transfer function. In this case, the network response can be expressed in closed form as a weighted power mean. The quadratic Scheffé K-polynomial and the exponential Wilson equation turn out to be special forms of this general mixture model. Advantages of the proposed network architecture are that binary data sets suffice for “training” and that it is readily extended to incorporate additional mixture components while retaining all previously determined weights.

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A PROBABILISTIC SELF-ORGANIZING MAP FOR BINARY DATA TOPOGRAPHIC CLUSTERING

International Journal of Computational Intelligence and Applications ◽

10.1142/s1469026808002351 ◽

2008 ◽

Vol 07 (04) ◽

pp. 363-383 ◽

Cited By ~ 10

Author(s):

MUSTAPHA LEBBAH ◽

YOUNÈS BENNANI ◽

NICOLETA ROGOVSCHI

Keyword(s):

Binary Data ◽

Learning Algorithm ◽

Data Sets ◽

Self Organizing Map ◽

Data Set ◽

Binary Coding ◽

Public Data ◽

Multivariate Binary Data ◽

Self Organizing

This paper introduces a probabilistic self-organizing map for topographic clustering, analysis and visualization of multivariate binary data or categorical data using binary coding. We propose a probabilistic formalism dedicated to binary data in which cells are represented by a Bernoulli distribution. Each cell is characterized by a prototype with the same binary coding as used in the data space and the probability of being different from this prototype. The learning algorithm, Bernoulli on self-organizing map, that we propose is an application of the EM standard algorithm. We illustrate the power of this method with six data sets taken from a public data set repository. The results show a good quality of the topological ordering and homogenous clustering.

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Estimation of excess volume and density of ternary liquid mixtures of non-electrolytes from binary data

Collection of Czechoslovak Chemical Communications ◽

10.1135/cccc19821414 ◽

1982 ◽

Vol 47 (5) ◽

pp. 1414-1419 ◽

Cited By ~ 263

Author(s):

Ivan Cibulka

Keyword(s):

Density Estimation ◽

Binary Data ◽

Excess Volume ◽

Maximum Error ◽

Liquid Mixtures ◽

Volume Estimation ◽

Ternary Mixtures ◽

Data Sets ◽

Mean Error ◽

The Mean

Several methods for estimating the excess volume and density of ternary liquid mixtures of non-electrolytes from binary data are tested using 27 sets of data from the literature. The mean error of the excess volume estimation is lower than 0.1 cm3 mol-1. The use of the tested methods for estimating the density of ternary mixtures results in a significant reduction of the error compared to the stimation when the mixture is considered to be ideal. In decisive majority of the data sets, the maximum error in the density estimation is lower than 0.1%.

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Critical Aspects of Person Counting and Density Estimation

Journal of Imaging ◽

10.3390/jimaging7020021 ◽

2021 ◽

Vol 7 (2) ◽

pp. 21

Author(s):

Roland Perko ◽

Manfred Klopschitz ◽

Alexander Almer ◽

Peter M. Roth

Keyword(s):

Density Estimation ◽

Network Architecture ◽

Reference Data ◽

State Of The Art ◽

Limit State ◽

Ground Truth ◽

Data Sets ◽

Ground Truth Generation ◽

Baseline Approach ◽

Critical Aspects

Many scientific studies deal with person counting and density estimation from single images. Recently, convolutional neural networks (CNNs) have been applied for these tasks. Even though often better results are reported, it is often not clear where the improvements are resulting from, and if the proposed approaches would generalize. Thus, the main goal of this paper was to identify the critical aspects of these tasks and to show how these limit state-of-the-art approaches. Based on these findings, we show how to mitigate these limitations. To this end, we implemented a CNN-based baseline approach, which we extended to deal with identified problems. These include the discovery of bias in the reference data sets, ambiguity in ground truth generation, and mismatching of evaluation metrics w.r.t. the training loss function. The experimental results show that our modifications allow for significantly outperforming the baseline in terms of the accuracy of person counts and density estimation. In this way, we get a deeper understanding of CNN-based person density estimation beyond the network architecture. Furthermore, our insights would allow to advance the field of person density estimation in general by highlighting current limitations in the evaluation protocols.

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Simultaneous confidence intervals for comparing margins of multivariate binary data

Computational Statistics & Data Analysis ◽

10.1016/j.csda.2013.02.016 ◽

2013 ◽

Vol 64 ◽

pp. 87-98 ◽

Cited By ~ 1

Author(s):

Bernhard Klingenberg ◽

Ville Satopää

Keyword(s):

Confidence Intervals ◽

Binary Data ◽

Simultaneous Confidence Intervals ◽

Multivariate Binary Data

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Density Estimation on Small Data Sets

Physical Review Letters ◽

10.1103/physrevlett.121.160605 ◽

2018 ◽

Vol 121 (16) ◽

Cited By ~ 5

Author(s):

Wei-Chia Chen ◽

Ammar Tareen ◽

Justin B. Kinney

Keyword(s):

Density Estimation ◽

Small Data ◽

Data Sets ◽

Small Data Sets

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Safe projections of binary data sets

Acta Informatica ◽

10.1007/s00236-006-0009-9 ◽

2006 ◽

Vol 42 (8-9) ◽

pp. 617-638 ◽

Cited By ~ 4

Author(s):

Nikolaj Tatti

Keyword(s):

Binary Data ◽

Data Sets

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Approximate confidence intervals for the difference in proportions for partially observed binary data

Statistical Methods in Medical Research ◽

10.1177/09622802211060528 ◽

2021 ◽

pp. 096228022110605

Author(s):

Ujjwal Das ◽

Ranojoy Basu

Keyword(s):

Binary Data ◽

Type I Error ◽

Missing At Random ◽

Matched Pair ◽

Data Sets ◽

Type I ◽

Real World Data ◽

Partially Observed ◽

The Difference ◽

Interval Estimator

We consider partially observed binary matched-pair data. We assume that the incomplete subjects are missing at random. Within this missing framework, we propose an EM-algorithm based approach to construct an interval estimator of the proportion difference incorporating all the subjects. In conjunction with our proposed method, we also present two improvements to the interval estimator through some correction factors. The performances of the three competing methods are then evaluated through extensive simulation. Recommendation for the method is given based on the ability to preserve type-I error for various sample sizes. Finally, the methods are illustrated in two real-world data sets. An R-function is developed to implement the three proposed methods.

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