A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Study on inequalities for multinomial variables.
We describe a simple and efficient procedure for approximating the Lévy measure of a random variable. We use this approximation to derive a finite sum-representation that converges almost surely to Ferguson's representation of the Dirichlet process based on arrivals of a homogeneous Poisson process.…
Develops a Bayesian method for causal inference with partly censored time-to-event data.
Generative model for high-dimensional categorical data using Gaussian-Dirichlet fields.
Sharp bounds for Dirichlet sums lead to improved Bayesian algorithm analysis.
Variational inference using the reparameterization trick has enabled large-scale approximate Bayesian inference in complex probabilistic models, leveraging stochastic optimization to sidestep intractable expectations. The reparameterization trick is applicable when we can simulate a random variable by applying a differ…
DrNAS improves neural architecture search with Dirichlet distribution and progressive learning.
To address the challenge of backpropagating the gradient through categorical variables, we propose the augment-REINFORCE-swap-merge (ARSM) gradient estimator that is unbiased and has low variance. ARSM first uses variable augmentation, REINFORCE, and Rao-Blackwellization to re-express the gradient as an expectation und…
Bayesian models that mix multiple Dirichlet prior parameters, called Multi-Dirichlet priors (MD) in this paper, are gaining popularity. Inferring mixing weights and parameters of mixed prior distributions seems tricky, as sums over Dirichlet parameters complicate the joint distribution of model parameters. This paper s…
A new method uses a product of experts with Dirichlet variables to approximate complex distributions.
DiAL uses Bayesian Dirichlet random fields for active learning with sparse labels.
Paper solves Dirichlet problem at infinity for Riemannian cones.
In this paper, we propose guaranteed spectral methods for learning a broad range of topic models, which generalize the popular Latent Dirichlet Allocation (LDA). We overcome the limitation of LDA to incorporate arbitrary topic correlations, by assuming that the hidden topic proportions are drawn from a flexible class o…
The Dirichlet random walk on manifolds has a positive escape rate if the cover is non-amenable.
Bayesian deep learning uses function-space priors to improve model uncertainty and robustness.
By providing a simple and efficient way of computing low-variance gradients of continuous random variables, the reparameterization trick has become the technique of choice for training a variety of latent variable models. However, it is not applicable to a number of important continuous distributions. We introduce an a…
A new method detects outliers using ensembles of Dirichlet process mixtures.
This study solves a Dirichlet problem for specific elliptic equations on Riemannian manifolds with concave boundaries.
Study on length distribution of random multicurves on large genus surfaces converging to Poisson-Dirichlet distribution.
Bayesian nonparametric approach for clustering non-exchangeable groups.
Bayesian nonparametric machine learning improves instrumental variable inference.
Tree structures are ubiquitous in data across many domains, and many datasets are naturally modelled by unobserved tree structures. In this paper, first we review the theory of random fragmentation processes [Bertoin, 2006], and a number of existing methods for modelling trees, including the popular nested Chinese rest…
Starting from an arbitrary sequence of polygons whose total perimeter is , we can build an (oriented) surface by pairing their sides in a uniform fashion. Chmutov and Pittel (arXiv:1503.01816) have shown that, regardless of the configuration of polygons we started with, the degree sequence of the graph obtained thi…
The paper compares one-hot encoding to Naïve Bayes for categorical variables.
Study on nonlinear elliptic equations with variable exponents, proving existence and multiplicity of solutions.
Brooks and Makover introduced an approach to studying the global geometric quantities (in particular, the first eigenvalue of the Laplacian, injectivity radius and diameter) of a ``typical'' compact Riemann surface of large genus based on compactifying finite-area Riemann surfaces associated with random cubic graphs; b…
In this paper, we propose novel strategies for neutral vector variable decorrelation. Two fundamental invertible transformations, namely serial nonlinear transformation and parallel nonlinear transformation, are proposed to carry out the decorrelation. For a neutral vector variable, which is not multivariate Gaussian d…
This paper proposes a generative model, the latent Dirichlet hidden Markov models (LDHMM), for characterizing a database of sequential behaviors (sequences). LDHMMs posit that each sequence is generated by an underlying Markov chain process, which are controlled by the corresponding parameters (i.e., the initial state …
We present a non-parametric Bayesian latent variable model capable of learning dependency structures across dimensions in a multivariate setting. Our approach is based on flexible Gaussian process priors for the generative mappings and interchangeable Dirichlet process priors to learn the structure. The introduction of…
Paper presents a reparameterized DP-DLGMM for clustering.
Bayesian test assesses dependence between mixed data types.
Geometric QHD tests improve hub detection in correlated data.
We propose the supervised hierarchical Dirichlet process (sHDP), a nonparametric generative model for the joint distribution of a group of observations and a response variable directly associated with that whole group. We compare the sHDP with another leading method for regression on grouped data, the supervised latent…
Community detection has been an active research area for decades. Among all probabilistic models, Stochastic Block Model has been the most popular one. This paper introduces a novel probabilistic model: RW-HDP, based on random walks and Hierarchical Dirichlet Process, for community extraction. In RW-HDP, random walks c…
We describe a nonparametric topic model for labeled data. The model uses a mixture of random measures (MRM) as a base distribution of the Dirichlet process (DP) of the HDP framework, so we call it the DP-MRM. To model labeled data, we define a DP distributed random measure for each label, and the resulting model genera…
Nonparametric mixture models based on the Dirichlet process are an elegant alternative to finite models when the number of underlying components is unknown, but inference in such models can be slow. Existing attempts to parallelize inference in such models have relied on introducing approximations, which can lead to in…
Corrected and improved simulation methods for Dirichlet-Laplace prior.
This paper analyzes MCMC algorithms on large graphs using Dirichlet forms.
AI-driven Bayesian inference improves decision-making uncertainty.
In latent Dirichlet allocation (LDA), topics are multinomial distributions over the entire vocabulary. However, the vocabulary usually contains many words that are not relevant in forming the topics. We adopt a variable selection method widely used in statistical modeling as a dimension reduction tool and combine it wi…
Abstract: Determines thermoelastic coefficients from boundary data.
Abstract: Generalizes SGMs to infinite-dimensional Hilbertian setting.
New method clusters directed and undirected graphs without losing directional information.
Approximate probabilistic inference algorithms are central to many fields. Examples include sequential Monte Carlo inference in robotics, variational inference in machine learning, and Markov chain Monte Carlo inference in statistics. A key problem faced by practitioners is measuring the accuracy of an approximate infe…
A new method for efficient BNC parameter estimation outperforms HDP smoothing.
We present the discrete infinite logistic normal distribution (DILN), a Bayesian nonparametric prior for mixed membership models. DILN is a generalization of the hierarchical Dirichlet process (HDP) that models correlation structure between the weights of the atoms at the group level. We derive a representation of DILN…
New neural network approach solves Poisson equations efficiently.
The latent Dirichlet allocation (LDA) model is a widely-used latent variable model in machine learning for text analysis. Inference for this model typically involves a single-site collapsed Gibbs sampling step for latent variables associated with observations. The efficiency of the sampling is critical to the success o…