We solve the mean parametrization of von Mises-Fisher distribution.
problem No closed-form normalization function for mean parameters exists.
method Derived a second-order ODE for mean normalizer and provided approximations.
result Rapid evaluation of densities and natural parameters in terms of mean parameters.
We present a derivation of the Kullback Leibler (KL)-Divergence (also known as Relative Entropy) for the von Mises Fisher (VMF) Distribution in d-dimensions.
Sparse prototypes improve clustering of high-dimensional directional data.
problem Clustering high-dimensional directional data like texts.
method Estimate a von Mises mixture using l1 penalized likelihood and EM algorithm.
result Sparse prototypes enhance interpretability and clustering performance.
Develops diffusion models for time-varying correlation on the circle.
problem Time-varying correlation modeling on the circle.
method Stochastic processes on the unit circle, specifically Brownian motion and von Mises diffusion.
result Derives an accurate analytical approximation to the transition density of the von Mises diffusion.
Researchers analyze SGD dynamics using von Mises-Fisher distributions.
problem Understanding the dynamics of stochastic gradient descent in high-dimensional spaces.
method Geometric analysis of minibatch gradient norms and directions through von Mises-Fisher distribution.
result Directional uniformity of minibatch gradients increases over SGD iterations.
Deep model generates high-quality speech from spectrograms.
problem Speech reconstruction from spectrograms.
method Deep generative model with Gaussian and von Mises distributions for magnitude and phase, variational autoencoder framework.
result Generated speech has high perceptual quality and intelligibility.
New method generates molecular conformations efficiently.
problem Generating accurate molecular conformations efficiently.
method Variational approximation of rotatable bond torsion angles as a mixture of von Mises distributions.
result VonMisesNet generates conformations orders of magnitude faster than existing methods.
A new method improves uncertainty quantification in Bayesian inference.
problem Poor uncertainty quantification in traditional Gibbs posteriors.
method Sequential Gibbs posteriors with a Bernstein-von Mises theorem.
result Sequential Gibbs posteriors provide better frequentist coverage.
Mixture modelling involves explaining some observed evidence using a combination of probability distributions. The crux of the problem is the inference of an optimal number of mixture components and their corresponding parameters. This paper discusses unsupervised learning of mixture models using the Bayesian Minimum M…
Bayesian UQ matches frequentist UQ for adaptively collected data.
problem Uncertainty quantification for adaptive data collection.
method Extends Bernstein-von Mises theorem to adaptively collected data.
result Bayesian UQ asymptotically matches Wald-type frequentist UQ.
New autoencoder improves latent space learning by optimizing sliced Gromov-Wasserstein discrepancies.
problem Improving inner discrepancy between prior and posterior distributions in autoencoders.
method Proposed spherical sliced fused Gromov Wasserstein (SSFG) and variants (MSSFG, PSSFG) to find important directions.
result New autoencoders achieve favorable performance in latent manifold learning, image generation, and reconstruction.
A new probabilistic approach improves deep metric learning by considering image uncertainties and class-specific variances.
problem Proxy-based deep metric learning struggles with image uncertainties and class-specific structures.
method Introduces non-isotropic probabilistic proxy-based deep metric learning using directional von Mises-Fisher distributions.
result Improves generalization performance and competitive on standard benchmarks.
New method uses fractional posteriors for semiparametric inference with improved uncertainty quantification.
problem Semiparametric inference with nonparametric priors and fractional posteriors.
method Established a general Bernstein--von Mises theorem for fractional posterior distributions, proposed shifted-and-rescaled credible sets.
result Fractional posterior credible sets provide reliable uncertainty quantification but have inflated size; shifted-and-rescaled set is an efficient confidence set.
A new method estimates the number of clusters on spherical data.
problem Estimating the number of clusters in spherical data.
method Spherical X-means (SX-means) method assuming von Mises-Fisher distributions.
result Shows the performance of SX-means in estimating the number of clusters.
Bagging is a device intended for reducing the prediction error of learning algorithms. In its simplest form, bagging draws bootstrap samples from the training sample, applies the learning algorithm to each bootstrap sample, and then averages the resulting prediction rules. We extend the definition of bagging from stati…
A new distance metric for vMF distributions simplifies spherical data analysis.
problem Intractability of normalization constants and lack of suitable geometric metrics for comparing vMF distributions.
method Proposes a Wasserstein-like distance that decomposes vMF distribution discrepancies into angular and concentration components.
result The proposed distance metric induces a latent geometric structure on the space of non-degenerate vMF distributions.
The modelling of empirically observed data is commonly done using mixtures of probability distributions. In order to model angular data, directional probability distributions such as the bivariate von Mises (BVM) is typically used. The critical task involved in mixture modelling is to determine the optimal number of co…
Proposes vMF distribution for skewed elliptical distributions.
problem Skewed distributions not adequately modeled by symmetric distributions.
method Introduces von-Mises-Fisher (vMF) distribution to represent skewed elliptical distributions.
result vMF distribution provides an explicit and simple probability representation of skewed elliptical distributions.
Circular variables arise in a multitude of data-modelling contexts ranging from robotics to the social sciences, but they have been largely overlooked by the machine learning community. This paper partially redresses this imbalance by extending some standard probabilistic modelling tools to the circular domain. First w…
Researchers identify valid auxiliary functions for extreme value distributions and their max-domains of attraction.
problem Characterize valid auxiliary functions for extreme value distributions and their max-domains of attraction.
method Introduced 'universal' auxiliary functions valid for both VR and vMR representations, identified sets of valid auxiliary functions, and proposed a method for finding appropriate auxiliary functions.
result Characterized valid auxiliary functions for both VR and vMR representations for the entire MDA distribution families.
Paper proposes a new loss function for training neural speech models.
problem Training high-performance neural speech waveform models.
method Uses short-time Fourier transform (STFT) spectra and assumes Gaussian and von Mises distributions for amplitude and phase spectra.
result Synthesized high-quality speech waveforms.
Optimized α-posteriors reduce KL divergence from true posterior in parametric misspecification.
problem Reduction of KL divergence from true posterior in parametric model misspecification.
method Derivation of Bernstein-von Mises theorem and optimization of α-posteriors. result Optimized α-posteriors minimize KL divergence from true posterior, especially in severe misspecification. The paper improves interpolation in generative models by using specific base distributions.
problem Unexpected side effects in linear interpolations of normalizing flows.
method Enforces a specific manifold using Dirichlet and von Mises-Fisher base distributions.
result Superior performance in terms of bits per dimension, FID, and KID scores for interpolation.
Deep Bayesian neural networks effectively select variables with rigorous uncertainty quantification.
problem High-dimensional variable selection with uncertainty.
method Developed new Bayesian non-parametric theorems for deep BNNs.
result BNNs can learn variable importance effectively in high dimensions and rigorously quantify uncertainty.
A new method for few-shot learning using directional statistics.
problem Few-shot classification with limited training data.
method Generates class representatives using a mixture of von Mises-Fisher distributions to capture inter-class correlation.
result Outperforms other methods in miniImageNet and tieredImageNet datasets.
A new method for speaker recognition on hyperspheres improves on PLDA's limitations.
problem Improving speaker recognition on hyperspheres with PLDA's limitations.
method Probabilistic Spherical Discriminant Analysis (PSDA) using Von Mises-Fisher distributions.
result PSDA scores are closed-form and can handle various trials, improving over PLDA.
A scalable method for accurate inference of low-dimensional parameters in high-dimensional linear regression.
problem Statistical inference for low-dimensional parameters in high-dimensional linear regression models.
method Mean-field variational Bayes approach, focusing on nuisance parameters and conditional distributions.
result Competitive numerical performance and theoretical guarantees for estimation and uncertainty quantification.
A drone-based MOT algorithm tracks vehicles using neural network detections and TPMBM filter.
problem Tracking multiple vehicles from drone-mounted cameras.
method Neural network for object detection, TPMBM filter for trajectory estimation, von-Mises Fisher distribution for DOA.
result TPMBM filter optimally estimates vehicle trajectories.
Solves parameter non-identifiability in Bayesian LTI system identification.
problem Parameter non-identifiability in standard Bayesian approaches for LTI system identification.
method Embedding canonical forms of LTI systems within the Bayesian framework.
result Unlocking the use of meaningful priors and robust uncertainty estimates.
New approach solves St. Petersburg paradox using randomness.
problem St. Petersburg paradox in game theory.
method Using Von Mises' axiom of randomness to determine cognitive strategies.
result Cognitive strategies can generate results not random, resolving paradox.
Bayesian model predicts circular data with fast Gibbs sampling.
problem Predicting circular data in scientific fields.
method Expressive von Mises quasi-processes with Stratonovich augmentation for posterior inference.
result Fast Gibbs sampling for posterior inference.
Improves Laplace approximation for Bayesian inference on Riemannian manifolds.
problem Inaccurate Gaussian approximations for complex targets and finite-data posteriors.
method Develops alternative variants of the Laplace approximation using a Riemannian metric.
result Exact approximations at the limit of infinite data, improving practical performance.
Paper shows DMS as an EM algorithm with improved convergence.
problem Improving the convergence of DMS algorithm.
method Shows DMS as a generalized EM algorithm and provides new proofs.
result Demonstrates global convergence and linear convergence of DMS.
Bayesian method for estimating ATE with robustness to model misspecification.
problem Estimating average treatment effects under unconfoundedness.
method Double robust Bayesian inference using adjusted prior and posterior distributions.
result Bayesian credible sets form asymptotically exact confidence intervals.
Markov chain Monte Carlo methods are often deemed too computationally intensive to be of any practical use for big data applications, and in particular for inference on datasets containing a large number n of individual data points, also known as tall datasets. In scenarios where data are assumed independent, various…
Generative models on spheres improve discrete sequence sampling.
problem Learning generative models for discrete sequences in continuous space.
method Work on sphere Sd−1, using von Mises-Fisher distribution and radial symmetry. result Improved results on Sudoku and language modeling with vMF path.
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 loss function speeds up sequence-to-sequence models for continuous outputs.
problem Slow and memory-intensive softmax layer limits vocabulary size and translation quality.
method Proposes a probabilistic loss and continuous embedding layer training/inference procedure.
result Models achieve up to 2.5x speed-up in training time with similar translation quality.
We propose a family of multivariate Gaussian process models for correlated outputs, based on assuming that the likelihood function takes the generic form of the multivariate exponential family distribution (EFD). We denote this model as a multivariate generalized Gaussian process model, and derive Taylor and Laplace al…
Bayesian model selection via mean-field variational approximation improves efficiency and accuracy.
problem Bayesian model selection under model mis-specification and latent variables.
method Mean-field variational approximation with non-asymptotic properties and geometric convergence.
result ELBO tends to select models closer to the true model than BIC as sample size increases.
The Variational Auto-Encoder (VAE) is one of the most used unsupervised machine learning models. But although the default choice of a Gaussian distribution for both the prior and posterior represents a mathematically convenient distribution often leading to competitive results, we show that this parameterization fails …
We propose a novel model for generating graphs similar to a given example graph. Unlike standard approaches that compute features of graphs in Euclidean space, our approach obtains features on a surface of a hypersphere. We then utilize a von Mises-Fisher distribution, an exponential family distribution on the surface …
Traditional topic models do not account for semantic regularities in language. Recent distributional representations of words exhibit semantic consistency over directional metrics such as cosine similarity. However, neither categorical nor Gaussian observational distributions used in existing topic models are appropria…
Bayesian inference corrected for bias in high-dimensional models.
problem Bayesian inference for high-dimensional regression models often produces biased credible sets.
method Debiasing approach based on Bernstein-von Mises theorem.
result Frequentist validity of debiased Bayesian posterior.
Researchers enhance hyperspherical latent representations for higher-dimensional data.
problem Limited expressivity of hyperspherical vMF distribution in high dimensions.
method Use a product-space to extend hyperspherical parameterizations to higher dimensions.
result Improved results on image datasets compared to traditional methods.
We revisit the Kolmogorov-Smirnov and Cramér-von Mises goodness-of-fit (GoF) tests and propose a generalisation to identically distributed, but dependent univariate random variables. We show that the dependence leads to a reduction of the "effective" number of independent observations. The generalised GoF tests are not…
We investigate the probability distributions of the recurrence intervals τ between consecutive 1-min returns above a positive threshold q>0 or below a negative threshold q<0 of two indices and 20 individual stocks in China's stock market. The distributions of recurrence intervals for positive and negative thresho…
We propose a new Integral Probability Metric (IPM) between distributions: the Sobolev IPM. The Sobolev IPM compares the mean discrepancy of two distributions for functions (critic) restricted to a Sobolev ball defined with respect to a dominant measure μ. We show that the Sobolev IPM compares two distributions in hig…