Using the Dirichlet model to predict how fashion brands compete and grow on eBay

In this paper, we present the following contributions: (i) an adaptation of a precise classifier to work on imprecise classification for cost-sensitive problems; (ii) a new measure to check the performance of an imprecise classifier. The imprecise classifier is based on a method to build simple decision trees that we have modified for imprecise classification. It uses the Imprecise Dirichlet Model (IDM) to represent information, with the upper entropy as a tool for splitting. Our new measure to compare imprecise classifiers takes errors into account. Thus far, this has not been considered by other measures for classifiers of this type. This measure penalizes wrong predictions using a cost matrix of the errors, given by an expert; and it quantifies the success of an imprecise classifier based on the cardinal number of the set of non-dominated states returned. To compare the performance of our imprecise classification method and the new measure, we have used a second imprecise classifier known as Naive Credal Classifier (NCC) which is a variation of the classic Naive Bayes using the IDM; and a known measure for imprecise classification.

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Reflection Method for Mathematical Modeling of Potential Fields in Multi-Layer Media

EPJ Web of Conferences ◽

10.1051/epjconf/201922401004 ◽

2019 ◽

Vol 224 ◽

pp. 01004

Author(s):

Oleg Yaremko ◽

Natalia Yaremko

Keyword(s):

Boundary Value Problems ◽

Boundary Value ◽

Field Potential ◽

Computer Code ◽

Potential Fields ◽

Reflection Method ◽

Dirichlet Problems ◽

Thermal Fields ◽

Dirichlet Model ◽

Fourth Kind

In this paper, potential fields in areas with plane and circular symmetry have been studied. In this case, the field potential is defined as the sum of solutions of Dirichlet model boundary value problems. The reflection method is used for the modeling of stationary thermal fields in multilayer media. By applying the reflection method, we found analytical solutions of boundary value problems with boundary conditions of the fourth kind for the Laplace equations and developed new computational algorithms. The developed algorithms can be easily implemented and transformed into a computer code. First of all, these algorithms implement consistent solutions of the Dirichlet problems for the model domains that allows using libraries of subroutines. Secondly, they have high algorithmic efficiency. It has been shown that reflection method is identical to the method of transformation operators and proved that transformation operator can be decomposed into a series of successive reflections from the external and internal boundaries. Finally, a physical interpretation of the reflection method has been discussed in detail.

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Excess Behavioral Loyalty for High-Share Brands: Deviations from the Dirichlet Model for Repeat Purchasing

Journal of Marketing Research ◽

10.2307/3172692 ◽

1993 ◽

Vol 30 (4) ◽

pp. 478 ◽

Cited By ~ 114

Author(s):

Peter S. Fader ◽

David C. Schmittlein

Keyword(s):

Behavioral Loyalty ◽

Dirichlet Model ◽

High Share ◽

Repeat Purchasing

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ACTOR: a latent Dirichlet model to compare expressed isoform proportions to a reference panel

10.1101/856401 ◽

2019 ◽

Author(s):

Sean D. McCabe ◽

Andrew B. Nobel ◽

Michael I. Love

Keyword(s):

Relative Proportion ◽

Disease Status ◽

R Package ◽

Tissue Expression ◽

Reference Panel ◽

Tissue Type ◽

Disease States ◽

Dirichlet Model ◽

Public Datasets ◽

Splicing Patterns

AbstractThe relative proportion of RNA isoforms expressed for a given gene has been associated with disease states in cancer, retinal diseases, and neurological disorders. Examination of relative isoform proportions can help determine biological mechanisms, but such analyses often require a per-gene investigation of splicing patterns. Leveraging large public datasets produced by genomic consortia as a reference, one can compare splicing patterns in a dataset of interest with those of a reference panel in which samples are divided into distinct groups (tissue of origin, disease status, etc). We propose ACTOR, a latent Dirichlet model with Dirichlet Multinomial observations to compare expressed isoform proportions in a dataset to an independent reference panel. We use a variational Bayes procedure to estimate posterior distributions for the group membership of one or more samples. Using the Genotype-Tissue Expression (GTEx) project as a reference dataset, we evaluate ACTOR on simulated and real RNA-seq datasets to determine tissue-type classifications of genes. ACTOR is publicly available as an R package at https://github.com/mccabes292/actor.

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Minimum Description Length Codes Are Critical

Entropy ◽

10.3390/e20100755 ◽

2018 ◽

Vol 20 (10) ◽

pp. 755 ◽

Cited By ~ 7

Author(s):

Ryan Cubero ◽

Matteo Marsili ◽

Yasser Roudi

Keyword(s):

Phase Transition ◽

Minimum Description Length ◽

Generative Models ◽

Restricted Boltzmann Machines ◽

Widespread Occurrence ◽

Generative Process ◽

Empirical Distributions ◽

Model Independent ◽

Dirichlet Model

In the Minimum Description Length (MDL) principle, learning from the data is equivalent to an optimal coding problem. We show that the codes that achieve optimal compression in MDL are critical in a very precise sense. First, when they are taken as generative models of samples, they generate samples with broad empirical distributions and with a high value of the relevance, defined as the entropy of the empirical frequencies. These results are derived for different statistical models (Dirichlet model, independent and pairwise dependent spin models, and restricted Boltzmann machines). Second, MDL codes sit precisely at a second order phase transition point where the symmetry between the sampled outcomes is spontaneously broken. The order parameter controlling the phase transition is the coding cost of the samples. The phase transition is a manifestation of the optimality of MDL codes, and it arises because codes that achieve a higher compression do not exist. These results suggest a clear interpretation of the widespread occurrence of statistical criticality as a characterization of samples which are maximally informative on the underlying generative process.

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