arXiv research

We solve the mean parametrization of von Mises-Fisher distribution.

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.

Develops diffusion models for time-varying correlation on the circle.

New method generates molecular conformations efficiently.

A new method improves uncertainty quantification in Bayesian inference.

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.

New autoencoder improves latent space learning by optimizing sliced Gromov-Wasserstein discrepancies.

A new probabilistic approach improves deep metric learning by considering image uncertainties and class-specific variances.

New method uses fractional posteriors for semiparametric inference with improved uncertainty quantification.

A new method estimates the number of clusters on spherical data.

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.

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.

This paper proposes an approach to the joint modeling of the short-time Fourier transform magnitude and phase spectrograms with a deep generative model. We assume that the magnitude follows a Gaussian distribution and the phase follows a von Mises distribution. To improve the consistency of the phase values in the time…

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.

Although stochastic gradient descent (SGD) is a driving force behind the recent success of deep learning, our understanding of its dynamics in a high-dimensional parameter space is limited. In recent years, some researchers have used the stochasticity of minibatch gradients, or the signal-to-noise ratio, to better char…

Optimized $\alpha$-posteriors reduce KL divergence from true posterior in parametric misspecification.

The paper improves interpolation in generative models by using specific base distributions.

A new method for speaker recognition on hyperspheres improves on PLDA's limitations.

A scalable method for accurate inference of low-dimensional parameters in high-dimensional linear regression.

A drone-based MOT algorithm tracks vehicles using neural network detections and TPMBM filter.

Solves parameter non-identifiability in Bayesian LTI system identification.

Bayesian model predicts circular data with fast Gibbs sampling.

Paper shows DMS as an EM algorithm with improved convergence.

Improves Laplace approximation for Bayesian inference on Riemannian manifolds.

Bayesian method for estimating ATE with robustness to model misspecification.

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.

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…

This work develops rigorous theoretical basis for the fact that deep Bayesian neural network (BNN) is an effective tool for high-dimensional variable selection with rigorous uncertainty quantification. We develop new Bayesian non-parametric theorems to show that a properly configured deep BNN (1) learns the variable im…

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.

In this article we will propose a completely new point of view for solving one of the most important paradoxes concerning game theory. The solution develop shifts the focus from the result to the strategy s ability to operate in a cognitive way by exploiting useful information about the system. In order to determine fr…

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 …

Learning suitable latent representations for observed, high-dimensional data is an important research topic underlying many recent advances in machine learning. While traditionally the Gaussian normal distribution has been the go-to latent parameterization, recently a variety of works have successfully proposed the use…

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.

Metric-based few-shot learning methods try to overcome the difficulty due to the lack of training examples by learning embedding to make comparison easy. We propose a novel algorithm to generate class representatives for few-shot classification tasks. As a probabilistic model for learned features of inputs, we consider…

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…

The distribution of trade sizes and trading volumes are investigated based on the limit order book data of 22 liquid Chinese stocks listed on the Shenzhen Stock Exchange in the whole year 2003. We observe that the size distribution of trades for individual stocks exhibits jumps, which is caused by the number preference…

Study of filtering and smoothing in submanifolds of Euclidean space.