Unleashing the Power of Dirichlet Distribution in Statistical Modeling

Jun 29, 2025

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Dive into the versatile applications of the Dirichlet distribution in statistical modeling, from Bayesian inference to natural language processing. Understand its significance in various fields and learn how to harness its power effectively.

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dirichlet distribution
statistical modeling
bayesian inference
natural language processing

wilmer

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Unleashing the Power of Dirichlet Distribution in Statistical Modeling

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Dirichlet:

An Introduction to Latent Dirichlet Allocation (LDA)

An Introduction to Latent Dirichlet Allocation (LDA). David M. Blei, Andrew Y. Ng, and Michael I. Jordan. Latent Dirichlet Allocation. Journal of Machine Learning Research 3 (2003): 993-1022. LDA. A generative probabilistic model for collections of discrete data such text corpora.

3.23k views • 55 slides

Simultaneous Diophantine Approximation with Excluded Primes

Simultaneous Diophantine Approximation with Excluded Primes. László Babai Daniel Štefankovič. Dirichlet (1842) Simultaneous Diophantine Approximation. Given reals. and . integers. such that and . for all . trivial. Simultaneous Diophantine Approximation

607 views • 41 slides

Hierarchical Dirichlet Process and Infinite Hidden Markov Model

Hierarchical Dirichlet Process and Infinite Hidden Markov Model. Paper by Y. W. Teh, M. I. Jordan, M. J. Beal & D. M. Blei, NIPS 2004. Duke University Machine Learning Group Presented by Kai Ni February 17, 2006. Outline. Motivation Dirichlet Processes (DP)

651 views • 19 slides

Unsupervised and Weakly-Supervised Probabilistic Modeling of Text

Unsupervised and Weakly-Supervised Probabilistic Modeling of Text. Ivan Titov April 23 2010. TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: A A A A A A A A A A A A. Outline. Topic Models: An Example of Latent Dirichlet Allocation

767 views • 64 slides

Random Walks for Image segmentation

Leo Grady, Member, IEEE. Random Walks for Image segmentation. IEEE Transaction on pattern analysis and machine intelligence, November 2006. Outline. Introduction Algorithm Dirichlet Problem Behavioral Properties Result--Demo. Introduction. K-way image segmentation

845 views • 37 slides

Lecture 6: Signal Processing III

Lecture 6: Signal Processing III. EEN 112: Introduction to Electrical and Computer Engineering. Professor Eric Rozier, 2/ 25/ 13. PIGEONS AND HOLES. Pigeonholes. The Pigeonhole Principle. First formalized by Johann Dirichlet in 1834 Schubfachprinzip (drawer principle)

501 views • 32 slides

An Introduction to LDA Tools

An Introduction to LDA Tools. Kuan -Yu Chen Institute of Information Science, Academia Sinica. Reference. D. M. Blei et al., “Latent Dirichlet allocation,” Journal of Machine Learning Research , 3, pp. 993–1022, January 2003 .

352 views • 22 slides

A Dirichlet -to-Neumann ( DtN ) Multigrid Algorithm for Locally Conservative Methods

A Dirichlet -to-Neumann ( DtN ) Multigrid Algorithm for Locally Conservative Methods . Mary F. Wheeler The University of Texas at Austin – ICES Tim Wildey Sandia National Labs SIAM Conference Computational and Mathematical Issues in the Geosciences March 21-24, 2011 Long Beach, CA.

667 views • 53 slides

Outline

Bayesian Hierarchical Clustering Paper by K. Heller and Z. Ghahramani ICML 2005 Presented by HAO-WEI, YEH . Outline. Background - Traditional Methods Bayesian Hierarchical Clustering (BHC) Basic ideas Dirichlet Process Mixture Model ( DPM) Algorithm Experiment results Conclusion.

526 views • 34 slides

Variational Inference for Dirichlet Process Mixture

Variational Inference for Dirichlet Process Mixture. Applied Bayesian Nonparametrics Special Topics in Machine Learning Brown University CSCI 2950-P, Fall 2011. Daniel Klein and Soravit Beer Changpinyo October 11, 2011. Motivation.

755 views • 39 slides

Analysis of Social Media MLD 10-802, LTI 11-772

Analysis of Social Media MLD 10-802, LTI 11-772. William Cohen 10- 16- 010. Review - LDA. “Mixed membership”. Latent Dirichlet Allocation. . Randomly initialize each z m,n Repeat for t=1,…. For each doc m, word n Find Pr( z mn = k |other z’s)

328 views • 22 slides

Random Walks for Image segmentation

548 views • 37 slides

Topic modeling experiments benchmark and simple evaluations

Topic modeling experiments benchmark and simple evaluations. 11 /15, 11/16 . What to measure. Empirical running time (1000 samplings) * Both Dirichlet and Logistic normal * Both a single prior and a mixture model

364 views • 22 slides

LECTURE 08: FOURIER SERIES

LECTURE 08: FOURIER SERIES. Objectives: Eigenfunctions Fourier Series of CT Signals Trigonometric Fourier Series Dirichlet Conditions Gibbs Phenomena Resources: Wiki: Fourier Series Wiki: Eigenfunctions OW: S&S (pp. 177-201) MIT 6.003: Lecture 5 Wolfram: Fourier Series Falstad : Java Applet.

421 views • 13 slides

Finite Element Analysis

Finite Element Analysis. Mathematical Background. http ://www.kmitl.ac.th/~ kpbumroo/12019801. One-Dimensional Computation Example. Second-Order One-Dimensional Linear Differential Equation Dirichlet boundary conditions Exact solution. Finite Difference Approximations. Forward difference

1.14k views • 64 slides

Preliminary Exam

Department of Electrical and Computer Engineering. Hierarchical Dirichlet Processes and Infinite HMMs. Submitted to: Dr. Joseph Picone, Examining Committee Chair Dr. Iyad Obeid, Committee Member, Depat . of Electrical and Computer Engineering

622 views • 30 slides

Amr Ahmed and Eric P. Xing

Dynamic Non-Parametric Mixture Models and The Recurrent Chinese Restaurant Process (SDM, 2008). Timeline: A Dynamic Hierarchical Dirichlet Process Model for Recovering Birth/Death and Evolution of Topics in Text Stream (UAI 2010). Amr Ahmed and Eric P. Xing. Presented by Bo Chen. Outiline.

535 views • 20 slides

Ratios

Ratios. June 4, 2009. Euler Product. To get the ratios conjecture. Follow the recipe for moments Replace the numerator L’s by apprx fnc eq Replace the denominator L’s by their full Dirichlet series Multiply out Bring the average over the family inside

756 views • 54 slides

Latent Dirichlet Allocation (LDA)

Latent Dirichlet Allocation (LDA). Week 8. Motivation. What do we want to do with text corpora? classification, novelty detection, summarization and similarity/relevance judgments. Given a text corpora or other collection of discrete data we wish to: Find a short description of the data.

1.04k views • 55 slides

Wavelet Transform and Some Applications in Time Series Analysis and Forecasting

Wavelet Transform and Some Applications in Time Series Analysis and Forecasting. A little bit of history…. Jean Baptiste Joseph Fourier (1768 – 1830). MGP: Leibniz - Bernoulli - Bernoulli - Euler - Lagrange - Fourier – Dirichlet - …. 1787: Train for priest (Left but Never married!!!).

505 views • 38 slides

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