Directly proves CRP from stick-breaking process without measure theory.
problem Indirect proof of CRP from stick-breaking process is complex.
method Direct proof using stick-breaking process to CRP, avoiding measure theory.
result Direct proof connects stick-breaking process to CRP.
SB-VAE uses Stick-Breaking processes for Bayesian nonparametric latent representations.
problem Learning latent representations with stochastic dimensionality.
method Stochastic Gradient Variational Bayes applied to Stick-Breaking processes.
result SB-VAE learns highly discriminative latent representations that outperform Gaussian VAE.
The beta-Bernoulli process provides a Bayesian nonparametric prior for models involving collections of binary-valued features. A draw from the beta process yields an infinite collection of probabilities in the unit interval, and a draw from the Bernoulli process turns these into binary-valued features. Recent work has …
Many data are naturally modeled by an unobserved hierarchical structure. In this paper we propose a flexible nonparametric prior over unknown data hierarchies. The approach uses nested stick-breaking processes to allow for trees of unbounded width and depth, where data can live at any node and are infinitely exchangeab…
A new Bayesian multinomial regression model using permuted and augmented stick-breaking.
problem Modeling categorical response variables given covariates.
method Permuted and augmented stick-breaking (paSB) construction.
result Transforms multinomial regression into regression of stick-specific binary variables.
The study assesses sensitivity to prior choices in Bayesian nonparametric models.
problem Difficulty in specifying priors for Bayesian nonparametric models.
method Utilizes variational Bayesian methods to assess sensitivity to concentration parameter and stick-breaking distribution.
result Demonstrates how to evaluate sensitivity to prior choices in Dirichlet process mixtures and related models.
Expectation maximization (EM) has recently been shown to be an efficient algorithm for learning finite-state controllers (FSCs) in large decentralized POMDPs (Dec-POMDPs). However, current methods use fixed-size FSCs and often converge to maxima that are far from optimal. This paper considers a variable-size FSC to rep…
We show that the stick-breaking construction of the beta process due to Paisley, et al. (2010) can be obtained from the characterization of the beta process as a Poisson process. Specifically, we show that the mean measure of the underlying Poisson process is equal to that of the beta process. We use this underlying re…
Improved Gaussian process experts model for complex data.
problem Limitations of standard Gaussian processes: scalability and predictive performance.
method Proposes a new mixture model of Gaussian process experts based on kernel stick-breaking processes.
result Improved predictive performance compared to existing models.
Paper proposes a VB method for TS-SBP mixture models with reduced computational cost.
problem Efficiently learning tree-structured stick-breaking process mixture models.
method Utilizes Bayes coding algorithm for context tree models to calculate sums over all possible trees.
result Proposes a learning algorithm with less computational cost for TS-SBP mixture of Gaussians.
While most Bayesian nonparametric models in machine learning have focused on the Dirichlet process, the beta process, or their variants, the gamma process has recently emerged as a useful nonparametric prior in its own right. Current inference schemes for models involving the gamma process are restricted to MCMC-based …
Many practical modeling problems involve discrete data that are best represented as draws from multinomial or categorical distributions. For example, nucleotides in a DNA sequence, children's names in a given state and year, and text documents are all commonly modeled with multinomial distributions. In all of these cas…
We introduce a new method to handle permutations efficiently using variational inference.
problem Efficient probabilistic reasoning about permutations in high-dimensional spaces.
method We reparameterize the Birkhoff polytope to enable variational inference over permutations.
result Our method enables efficient and accurate Bayesian inference over permutations.
A new method improves posterior approximation for complex distributions.
problem Difficulty in capturing multimodal and heavy-tailed posteriors with standard normalizing flows.
method StiCTAF: stick-breaking mixture base with component-wise tail adaptation.
result Improved tail recovery and better mode coverage compared to benchmarks.
Nonparametric Bayesian approaches to clustering, information retrieval, language modeling and object recognition have recently shown great promise as a new paradigm for unsupervised data analysis. Most contributions have focused on the Dirichlet process mixture models or extensions thereof for which efficient Gibbs sam…
The paper models financial returns data with measurement error.
problem Modeling measurement error in financial returns data.
method Develops a stochastic model using a Lévy process and approximates the joint transition density via a stick-breaking representation. Implements MCMC and multilevel MCMC algorithms.
result Provides an approximation and sampling methods for Bayesian parameter estimation of the model.
Infinite hierarchical contrastive clustering identifies personal environments linked to health outcomes.
problem Identifying meaningful relationships between environmental features and health outcomes on an individual level.
method Contrastive clustering framework with stick-breaking prior and participant-specific prediction loss.
result Model effectively identifies distinct personal environments and groups them into meaningful types linked to health outcomes.
The paper extends and applies a new shrinkage prior in Bayesian factor analysis.
problem Estimating the number of factors in sparse Bayesian factor analysis.
method Introduces and extends a generalized cumulative shrinkage process (CUSP) prior.
result Exchangeable spike-and-slab shrinkage priors imply increasing shrinkage as the column index increases.
This paper proposes a Hilbert space embedding for Dirichlet Process mixture models via a stick-breaking construction of Sethuraman. Although Bayesian nonparametrics offers a powerful approach to construct a prior that avoids the need to specify the model size/complexity explicitly, an exact inference is often intractab…
In this work, we propose the kernel Pitman-Yor process (KPYP) for nonparametric clustering of data with general spatial or temporal interdependencies. The KPYP is constructed by first introducing an infinite sequence of random locations. Then, based on the stick-breaking construction of the Pitman-Yor process, we defin…
A new model sHDP adds smoothness constraints to HDP for evolving mixture densities.
problem Evolution of mixture densities in time-varying scenarios.
method Smoothed Hierarchical Dirichlet Process (sHDP) with temporal constraints.
result Inference algorithm and experimental validation on NIPS keywords.
We introduce the nonparametric metadata dependent relational (NMDR) model, a Bayesian nonparametric stochastic block model for network data. The NMDR allows the entities associated with each node to have mixed membership in an unbounded collection of latent communities. Learned regression models allow these memberships…
New techniques model related samples using kernel mixtures, addressing shared and varying components with misalignments.
problem Modeling related samples with shared and varying components, accounting for misalignments.
method Introduces ψ-stick breaking for mixing weights and kernel perturbation for misalignment. result Efficient Bayesian inference for models incorporating these techniques.
Statistical machine learning methods, especially nonparametric Bayesian methods, have become increasingly popular to infer clonal population structure of tumors. Here we describe the treeCRP, an extension of the Chinese restaurant process (CRP), a popular construction used in nonparametric mixture models, to infer the …
New distribution on simplex for auto-encoding tasks.
problem Developing a new distribution for sparsity in auto-encoding models.
method Using Kumaraswamy distribution and ordered stick-breaking process.
result The new distribution has an exact and closed form reparameterization.
A new method to estimate local volatility from high-frequency data.
problem Quantitative trading risk management needs a better way to estimate volatility.
method Realized local volatility surface estimated via high-frequency data and Bayesian nonparametric estimation.
result The method can capture counterfactual volatility and improve risk management.
A new memory-efficient sign language translation model reduces weight usage.
problem Memory constraints in real-time sign language translation.
method Variational Bayesian sequence-to-sequence network with Gaussian posterior and Indian Buffet Process prior.
result The proposed model achieves substantial weight compression without compromising performance.
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…
A tree-based dictionary learning model is developed for joint analysis of imagery and associated text. The dictionary learning may be applied directly to the imagery from patches, or to general feature vectors extracted from patches or superpixels (using any existing method for image feature extraction). Each image is …
A new method reparameterizes Gaussian noise for better flexibility and performance.
problem Improving the Gumbel-Softmax for better flexibility and performance.
method Invertible Gaussian Reparameterization (IGR) using modified softmax and transformations.
result IGR outperforms Gumbel-Softmax in various experiments.
Bayesian nonparametric approach for clustering non-exchangeable groups.
problem Clustering grouped data with dependencies among groups.
method Graphical Dirichlet process modeling with Markov property.
result Efficient posterior inference algorithm developed.
Model improves surgical complication prediction using latent factor learning.
problem Tackles prediction of surgical complications.
method Transfer learning via latent factor modeling.
result Improves risk assessment model for surgery patients.
New gradient estimators for discrete variables improve model training.
problem Training models with discrete latent variables is challenging due to high gradient variance.
method Introduced novel gradient estimators based on importance sampling and statistical couplings, extending to categorical variables.
result Proposed gradient estimators outperform previous methods in systematic experiments.
Bayesian deep networks with local competition reduce model complexity without sacrificing accuracy.
problem Inference of deep networks with minimal model complexity.
method Revisits deep networks with local competition, using Bayesian nonparametrics for inference of connections and precision.
result Yields networks with less computational footprint and no accuracy loss.
New deep learning model robust to adversarial attacks using stochastic LWTA units.
problem Adversarial robustness in deep learning networks.
method Introduces deep networks with stochastic LWTA activations, combining them with Bayesian non-parametric tools.
result Achieves high robustness to adversarial perturbations, outperforming state-of-the-art methods.
New model improves deep learning robustness against adversarial attacks.
problem Improving adversarial robustness of deep learning models.
method Local competition principle, LWTA nonlinearities, Bayesian non-parametrics.
result The new model achieves high robustness to adversarial perturbations on MNIST and CIFAR10 datasets.
Method simulates drawdown and duration in Lévy models using Gaussian approximation.
problem Simulating drawdown and duration in Lévy models with high jump activity.
method Stick-breaking Gaussian approximation for simulation, bounds on Wasserstein distances.
result Good agreement between theoretical bounds and numerical performance.
DPPS uses DP priors for Bayesian non-parametric multi-arm bandits.
problem Optimizing multi-arm bandit environments with prior beliefs.
method Bayesian non-parametric algorithm based on Dirichlet Process priors.
result DPPS provides principled incorporation of prior beliefs and is optimal in Bayesian regret setup.
A new method for embedding sparse high-order interactions.
problem Learning embeddings from sparse high-order interaction events.
method Hybridizing sparse hypergraph and matrix Gaussian processes.
result Strong asymptotic bounds on sparsity ratio.
In cargo logistics, a key performance measure is transport risk, defined as the deviation of the actual arrival time from the planned arrival time. Neither earliness nor tardiness is desirable for customer and freight forwarders. In this paper, we investigate ways to assess and forecast transport risks using a half-yea…
Proposes Dirichlet Variational Autoencoder (DirVAE) for better latent representation.
problem Improving latent representation in autoencoders.
method Uses Dirichlet prior and stochastic gradient method with inverse Gamma approximation to address collapsing issues.
result DirVAE outperforms baselines in log-likelihood and classification accuracy.
New framework learns complex AI attitudes from heterogeneous data.
problem Heterogeneous ordinal structure in AI attitudes, poorly captured by existing methods.
method Monotone Gaussian score embedding, BNP complexity discovery, confirmatory fixed-K estimation.
result Reduced holdout MSE by 25.8% over single-graph baseline.
GENESIS-V2 infers unordered object representations without iterative refinement.
problem Unsupervised learning of unordered object representations for complex images.
method Stochastic stick-breaking process for clustering pixel embeddings.
result GENESIS-V2 outperforms recent baselines in unsupervised image segmentation and scene generation.
Improved model for analyzing topics, sentiments, and user preferences in online reviews.
problem Inefficient processing of large-scale online review datasets.
method Developed variational inference models (vTSPRA, svTSPRA, ovTSPRA) for faster and more efficient processing of large datasets.
result The new models (svTSPRA, ovTSPRA) achieve better performance and faster convergence compared to the original TSPRA model.
Bayesian model predicts tooth disease counts with multiway structure.
problem Predicting disease counts across multiple tooth types for each patient.
method Nonparametric Bayesian approach with Dirichlet Process mixture model for clustered binomial data.
result Model outperforms competitors and provides interpretable results.
Flexible nonparametric model for discrete choice analysis.
problem Modeling heterogeneity in discrete choice data without fixed component limits.
method Dirichlet process mixture model with expectation maximisation algorithm.
result Proposed model outperforms latent class MNL and mixed MNL models in both fit and predictive ability.
New method reduces memory usage for high-dimensional variable selection.
problem Scalability issues in high-dimensional variable selection, especially in genomics.
method Adaptive sampling of null features to eliminate dummy matrix materialization.
result Reduces memory and runtime by several orders of magnitude while preserving FDR control.
Proposes CHDP for modeling cooperative hierarchical structures with Dirichlet processes.
problem Lack of flexible topic modeling for cooperative hierarchical structures.
method Introduces Cooperative Hierarchical Dirichlet Processes (CHDP) with superposition and maximization measures.
result Demonstrates improved modeling of cooperative hierarchical structures with CHDP.