Estimating a Dirichlet distribution

By Tom Minka. 2012

884 citations recorded by the source corpus.

Subfields: Statistics and Probability, Probabilistic & Bayesian Methods

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Citations in the corpus

How To Backdoor Federated Learning (2018, methodology): “training data and supply each participant with an unbalanced sample from each class, we divide the 50,000 training images using a Dirichlet distribution [46] with hyperparameter 0.”
Fast Distribution To Real Regression (2013, methodology): “Maximum likelihood parameter estimation for α, given a set of Dirichlet samples, is often performed via iterative optimization algorithms, such as gradient ascent or Newton’s method [8], as a closed form solution for the MLE does not appear to exist in the literature.”
Lightweight Probabilistic Deep Networks (2018, methodology): “Hence, inspired by [38], we reparametrize the Dirichlet distribution as (cid:16) X (cid:17) where ϑ = ( m , s ) are n location and a scale parameter, respectively.”
Group Anomaly Detection using Flexible Genre Models (2011, methodology): “, the topic distributions having genre t), which can be solved using the Newton–Raphson method [18].”
Weakly Supervised Joint Sentiment-Topic Detection from Text (2012, background): “estimation [26] and updated every 25 iterations during the”
Introduction to the Dirichlet Distribution and Related Processes (2010, methodology): “See [3] for details on how to use the expectation-maximization (EM) algorithm for this problem and [10] for a broader discussion including using Newton-Raphson.”
Latent Dirichlet Allocation Models for Image Classification (2013, methodology): “This optimization can be carried out by the method of Newton-Raphson, as detailed in [15].”
Back to the Drawing Board: A Critical Evaluation of Poisoning Attacks on Production Federated Learning (2021, methodology): “Unless speciﬁed otherwise, we consider 1,000 total FL clients and divide the 50,000 training data using Dirichlet distribution [42] with α = 1 .”
Self-Distillation as Instance-Specific Label Smoothing (2020, background): “Now, due to conjugacy of the Dirichlet prior, the marginal likelihood p(y|x;↵x) is a Dirichlet-multinomial distribution [26].”
DBA: Distributed Backdoor Attacks against Federated Learning (2020, methodology): “Here, we use a Dirichlet distribution (Minka, 2000) with different hyperparameter α to generate different data distribution following the setups in (Bagdasaryan et al.”
Learning cross-modality similarity for multinomial data (2011, background): “, in a slice during the Gibbs sampling procedure) [12].”
Dirichlet Variational Autoencoder (2019, positive): “We choose this estimator because of its closed form nature and consistency (Minka, 2000).”
Deep Anomaly Detection Using Geometric Transformations (2018, methodology): “, k−1}, we estimate α̃i using the fixed point iteration method described in [21], combined with the initialization step proposed by Wicker et al.”
A Latent Variable Model for Geographic Lexical Variation (2010, background): “The symmetric Dirichlet prior on θ is set to 1 2 , and the symmetric Dirichlet parameter on θ is updated from weak hyperpriors (Minka, 2003).”
Structured Stochastic Variational Inference (2014, methodology): “The product of the inverse of the Fisher matrix and a vector can therefore be computed in O(V ) time using the matrix inversion lemma (Minka, 2000).”
You Are What You Tweet: Analyzing Twitter for Public Health (2011, methodology): “We optimize s to maximize data likelihood using the fixed-point iteration derived by Minka (2003) to update the precision given a fixed mean.”
Social Collaborative Viewpoint Regression with Explainable Recommendations (2017, methodology): “Using two bounds defined in [27], we derive the following update rule for obtaining each user u’s optimized viewpoint distribution in Eq.”
Fashion Coordinates Recommender System Using Photographs from Fashion Magazines (2011, methodology): “The parameters α and β ( r ) can be estimated by maximizing the joint distribution (1) by using the ﬁxed-point iteration method described in [Minka, 2000] as follows: .”