Dirichlet distribution ≈ Dirichlet distribution
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A correlated topic model of Science Open
Topic models, such as latent Dirichlet allocation (LDA), can be useful tools for the statistical analysis of document collections and other discrete data. The LDA model assumes that the words of each document arise from a mixture of topics…
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Analysing continuous proportions in ecology and evolution: A practical introduction to beta and Dirichlet regression Open
Proportional data, in which response variables are expressed as percentages or fractions of a whole, are analysed in many subfields of ecology and evolution. The scale‐independence of proportions makes them appropriate to analyse many biol…
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Evidential Deep Learning to Quantify Classification Uncertainty Open
Deterministic neural nets have been shown to learn effective predictors on a wide range of machine learning problems. However, as the standard approach is to train the network to minimize a prediction loss, the resultant model remains igno…
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Fast hierarchical Bayesian analysis of population structure Open
We present fastbaps, a fast solution to the genetic clustering problem. Fastbaps rapidly identifies an approximate fit to a Dirichlet process mixture model (DPM) for clustering multilocus genotype data. Our efficient model-based clustering…
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Mixture Models With a Prior on the Number of Components Open
A natural Bayesian approach for mixture models with an unknown number of components is to take the usual finite mixture model with symmetric Dirichlet weights, and put a prior on the number of components—that is, to use a mixture of finite…
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Bayesian Regression Trees for High-Dimensional Prediction and Variable Selection Open
Decision tree ensembles are an extremely popular tool for obtaining high-quality predictions in nonparametric regression problems. Unmodified, however, many commonly used decision tree ensemble methods do not adapt to sparsity in the regim…
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Beyond temperature scaling: Obtaining well-calibrated multiclass probabilities with Dirichlet calibration Open
Class probabilities predicted by most multiclass classifiers are uncalibrated, often tending towards over-confidence. With neural networks, calibration can be improved by temperature scaling, a method to learn a single corrective multiplic…
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Mixing Dirichlet Topic Models and Word Embeddings to Make lda2vec Open
Distributed dense word vectors have been shown to be effective at capturing token-level semantic and syntactic regularities in language, while topic models can form interpretable representations over documents. In this work, we describe ld…
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Theory-Driven Analysis of Large Corpora: Semisupervised Topic Classification of the UN Speeches Open
There is a growing interest in quantitative analysis of large corpora among the international relations (IR) scholars, but many of them find it difficult to perform analysis consistently with existing theoretical frameworks using unsupervi…
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Maximum Likelihood Estimation of Functionals of Discrete Distributions Open
The Dirichlet prior is widely used in estimating discrete distributions and\nfunctionals of discrete distributions. In terms of Shannon entropy estimation,\none approach is to plug-in the Dirichlet prior smoothed distribution into the\nent…
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5 Spectral geometry of the Steklov problem Open
The Steklov problem is an eigenvalue problem with the spectral parameter in the boundary conditions, which has various applications. Its spectrum coincides with that of the Dirichlet-to-Neumann operator. Over the past years, there has been…
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Local Elliptic Regularity for the Dirichlet Fractional Laplacian Open
We prove the Wloc2s,p${W_{{\mathrm{loc}}}^{2s,p}}$ local elliptic regularity of weak solutions to the Dirichlet problem associated with the fractional Laplacian on an arbitrary bounded open set of ℝN${\mathbb{R}^{N}}$. The key tool consis…
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Riemann zeta fractional derivative—functional equation and link with primes Open
This paper outlines further properties concerning the fractional derivative of the Riemann ζ function. The functional equation, computed by the introduction of the Grünwald–Letnikov fractional derivative, is rewritten in a simplified form …
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A Note on Over-Smoothing for Graph Neural Networks Open
Graph Neural Networks (GNNs) have achieved a lot of success on graph-structured data. However, it is observed that the performance of graph neural networks does not improve as the number of layers increases. This effect, known as over-smoo…
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A Correlated Topic Model Using Word Embeddings Open
Conventional correlated topic models are able to capture correlation structure among latent topics by replacing the Dirichlet prior with the logistic normal distribution. Word embeddings have been proven to be able to capture semantic regu…
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Zero-inflated generalized Dirichlet multinomial regression model for microbiome compositional data analysis Open
Summary There is heightened interest in using high-throughput sequencing technologies to quantify abundances of microbial taxa and linking the abundance to human diseases and traits. Proper modeling of multivariate taxon counts is essentia…
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Unifying rational models of categorization via the hierarchical Dirichlet process Open
Models of categorization make different representational assumptions, with categories being represented by prototypes, sets of exemplars, and everything in between. Rational models of categorization justify these representational assumptio…
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Better latent spaces for better autoencoders Open
Autoencoders as tools behind anomaly searches at the LHC have the structural problem that they only work in one direction, extracting jets with higher complexity but not the other way around. To address this, we derive classifiers from the…
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Von Mises-Fisher Clustering Models Open
This paper proposes a suite of models for clustering high-dimensional data on a unit sphere based on von Mises-Fisher (vMF) distribution and for discovering more intuitive clusters than existing approaches. The proposed models include a) A…
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Ldagibbs: A Command for Topic Modeling in Stata Using Latent Dirichlet Allocation Open
In this article, I introduce the ldagibbs command, which implements latent Dirichlet allocation in Stata. Latent Dirichlet allocation is the most popular machine-learning topic model. Topic models automatically cluster text documents into …
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Multiple solutions for parametric double phase Dirichlet problems Open
We consider a parametric double phase Dirichlet problem. Using variational tools together with suitable truncation and comparison techniques, we show that for all parametric values [Formula: see text] the problem has at least three nontriv…
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$\alpha $-variational inference with statistical guarantees Open
We provide statistical guarantees for a family of variational approximations to Bayesian posterior distributions, called $\\alpha $-VB, which has close connections with variational approximations of tempered posteriors in the literature. T…
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Positive solutions for nonlinear singular elliptic equations of p-Laplacian type with dependence on the gradient Open
In this paper, we study a nonlinear Dirichlet problem of p-Laplacian type with combined effects of nonlinear singular and convection terms. An existence theorem for positive solutions is established as well as the compactness of solution s…
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Global threshold dynamics of an infection age-structured SIR epidemic model with diffusion under the Dirichlet boundary condition Open
In this paper, we are concerned with the global asymptotic behavior of an infection age-structured SIR epidemic model with diffusion in a general n-dimensional bounded spatial domain under the homogeneous Dirichlet boundary condition. By u…
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An initial-boundary value problem for the integrable spin-1 Gross-Pitaevskii equations with a 4 × 4 Lax pair on the half-line Open
We extend the idea of the Fokas unified transform to investigate the initial-boundary value problem for the integrable spin-1 Gross-Pitaevskii equations with a 4 × 4 Lax pair on the half-line. The solution of this system can be expressed i…
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Increasing stability for the inverse source scattering problem with multi-frequencies Open
Consider the scattering of the two-or three-dimensional Helmholtz equation where the source of the electric current density is assumed to be compactly supported in a ball. This paper concerns the stability analysis of the inverse source sc…
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Discretizations of the Spectral Fractional Laplacian on General Domains with Dirichlet, Neumann, and Robin Boundary Conditions Open
In this work, we propose novel discretisations of the spectral fractional Laplacian on bounded domains based on the integral formulation of the operator via the heat-semigroup formalism. Specifically, we combine suitable quadrature formula…
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Normalized concentrating solutions to nonlinear elliptic problems Open
We prove the existence of solutions (λ,v)∈R×H1(Ω) of the elliptic problem {−Δv+(V(x)+λ)v=vp in Ω,v>0,∫Ωv2dx=ρ. Any v solving such problem (for some λ) is called a normalized solution, where the normalization is settled in L2(Ω). Here Ω is …
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Global Very Weak Solutions to a Chemotaxis-Fluid System with Nonlinear Diffusion Open
We consider the chemotaxis-fluid system\n\\begin{align}\\label{star}\\tag{$\\diamondsuit$} \\left\\{\n\\begin{array}{r@{\\,}c@{\\,}c@{\\ }l@{\\quad}l@{\\quad}l@{\\,}c}\nn_{t}&+&u\\cdot\\!\\nabla n&=\\Delta n^m-\\nabla\\!\\cdot(n\\nabla c),…
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Liouville type theorems for the steady axially symmetric Navier-Stokes and magnetohydrodynamic equations Open
In this paper we study Liouville properties of smooth steady axially symmetric solutions of the Navier-Stokes equations.First, we provide another version of the Liouville theorem of [14] in the case of zero swirl, where we replaced the Dir…