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This research proposes a flexible Bayesian extension of the composite Gaussian process (CGP) model of Ba and Joseph (2012) for predicting (stationary or) non-stationary $y(\mathbf{x})$. The CGP generalizes the regression plus stationary…

Vecchia's approximate likelihood for Gaussian process parameters depends on how the observations are ordered, which can be viewed as a deficiency because the exact likelihood is permutation-invariant. This article takes the alternative…

While the success of pre-trained language models has largely eliminated the need for high-quality static word vectors in many NLP applications, such vectors continue to play an important role in tasks where words need to be modelled in the…

Dinatural transformations, which generalise the ubiquitous natural transformations to the case where the domain and codomain functors are of mixed variance, fail to compose in general; this has been known since they were discovered by Dubuc…

We present a novel approach for explaining Gaussian processes (GPs) that can utilize the full analytical covariance structure present in GPs. Our method is based on the popular solution concept of Shapley values extended to stochastic…

Variational inference is a powerful tool for approximate inference, and it has been recently applied for representation learning with deep generative models. We develop the variational Gaussian process (VGP), a Bayesian nonparametric…

Generalized numberings are an extension of Ershov's notion of numbering, based on partial combinatory algebra (pca) instead of the natural numbers. We study various algebraic properties of generalized numberings, relating properties of the…

In this paper we propose a simple yet powerful method for learning representations in supervised learning scenarios where each original input datapoint is described by a set of vectors and their associated outputs may be given by soft…

This article offers a simplified approach to the distribution theory of randomly weighted averages or $P$-means $M_P(X):= \sum_{j} X_j P_j$, for a sequence of i.i.d.random variables $X, X_1, X_2, \ldots$, and independent random weights $P:=…

We establish the Level-1 and Level-3 Large Deviation Principles (LDPs) for invariant measures on shift spaces over finite alphabets under very general decoupling conditions for which the thermodynamic formalism does not apply. Such…

Determinantal point processes (DPPs), which arise in random matrix theory and quantum physics, are natural models for subset selection problems where diversity is preferred. Among many remarkable properties, DPPs offer tractable algorithms…

The Generalized Mallows Model (GMM) is a well known family of models for ranking data. A GMM is a distribution over $\mathbb{S}_n$, the set of permutations of n objects, characterized by a location parameter $\sigma \in \mathbb{S}_n$, known…

Domain generalization (DG) aims at generalizing a classifier trained on multiple source domains to an unseen target domain with domain shift. A common pervasive theme in existing DG literature is domain-invariant representation learning…

Gaussian Processes (GPs) can be used as flexible, non-parametric function priors. Inspired by the growing body of work on Normalizing Flows, we enlarge this class of priors through a parametric invertible transformation that can be made…

In January 1969, Peter M. Neumann wrote a paper entitled "Primitive permutation groups of degree 3p". The main theorem placed restrictions on the parameters of a primitive but not 2-transitive permutation group of degree three times a…

The dictionary learning problem concerns the task of representing data as sparse linear sums drawn from a smaller collection of basic building blocks. In application domains where such techniques are deployed, we frequently encounter…

Every k entries in a permutation can have one of k! different relative orders, called patterns. How many times does each pattern occur in a large random permutation of size n? The distribution of this k!-dimensional vector of pattern…

In this paper, we provide a theoretical understanding of word embedding and its dimensionality. Motivated by the unitary-invariance of word embedding, we propose the Pairwise Inner Product (PIP) loss, a novel metric on the dissimilarity…

Due to domain shift, deep neural networks (DNNs) usually fail to generalize well on unknown test data in practice. Domain generalization (DG) aims to overcome this issue by capturing domain-invariant representations from source domains.…

Models for human choice prediction in preference learning and psychophysics often consider only binary response data, requiring many samples to accurately learn preferences or perceptual detection thresholds. The response time (RT) to make…