Related papers: Random Function Priors for Correlation Modeling
High-dimensional feature vectors are likely to contain sets of measurements that are approximate replicates of one another. In complex applications, or automated data collection, these feature sets are not known a priori, and need to be…
This report introduces general ideas and some basic methods of the Bayesian probability theory applied to physics measurements. Our aim is to make the reader familiar, through examples rather than rigorous formalism, with concepts such as:…
A density matrix describes the statistical state of a quantum system. It is a powerful formalism to represent both the quantum and classical uncertainty of quantum systems and to express different statistical operations such as measurement,…
Let $X=\{X_n: n\in \mathbb{N}\}$ be a linear process with bounded probability density function $f(x)$. Under certain conditions, we use the kernel estimator \[ \frac{2}{n(n-1)h_n} \sum_{1\le i<j\le n}K\Big(\frac{X_i-X_j}{h_n}\Big) \] to…
Model change detection is studied, in which there are two sets of samples that are independently and identically distributed (i.i.d.) according to a pre-change probabilistic model with parameter $\theta$, and a post-change model with…
Many pre-trained models (PTMs) are available in modern applications. Because different PTMs are often trained on different datasets, their performances can vary substantially for different new tasks, and the ranking of the candidates may…
Tensor-valued data are being encountered increasingly more commonly, in the biological, natural as well as the social sciences. The learning of the unknown model parameter vector given such data, involves covariance modelling of such data,…
In this paper, we propose an information-theoretic approach to design the functional representations to extract the hidden common structure shared by a set of random variables. The main idea is to measure the common information between the…
Parametric Embedding (PE) has recently been proposed as a general-purpose algorithm for class visualisation. It takes class posteriors produced by a mixture-based clustering algorithm and projects them in 2D for visualisation. However,…
We consider an ensemble of $K$ single-layer perceptrons exposed to random inputs and investigate the conditions under which the couplings of these perceptrons can be chosen such that prescribed correlations between the outputs occur. A…
The Nyman-Beurling criterion is an approximation problem in the space of square integrable functions on $(0,\infty)$, which is equivalent to the Riemann hypothesis. This involves dilations of the fractional part function by factors…
Large self-supervised models pretrained on millions of protein sequences have recently gained popularity in generating embeddings of protein sequences for protein function prediction. However, the absence of random baselines makes it…
Topic modelling was mostly dominated by Bayesian graphical models during the last decade. With the rise of transformers in Natural Language Processing, however, several successful models that rely on straightforward clustering approaches in…
Connectivity estimation is challenging in the context of high-dimensional data. A useful preprocessing step is to group variables into clusters, however, it is not always clear how to do so from the perspective of connectivity estimation.…
Many Natural Language Processing applications nowadays rely on pre-trained word representations estimated from large text corpora such as news collections, Wikipedia and Web Crawl. In this paper, we show how to train high-quality word…
Representation learning plays a crucial role in automated feature selection, particularly in the context of high-dimensional data, where non-parametric methods often struggle. In this study, we focus on supervised learning scenarios where…
Many of the data, particularly in medicine and disease mapping are count. Indeed, the under or overdispersion problem in count data distrusts the performance of the classical Poisson model. For taking into account this problem, in this…
We propose two classes of nonparametric point estimators of $\theta=P(X<Y)$ in the case where $(X,Y)$ are paired, possibly dependent, absolutely continuous random variables. The proposed estimators are based on nonparametric estimators of…
We reconsider the problem of calculating a general spectral correlation function containing an arbitrary number of products and ratios of characteristic polynomials for a N x N random matrix taken from the Gaussian Unitary Ensemble (GUE).…
A new class of dependent random measures which we call {\it compound random measures} are proposed and the use of normalized versions of these random measures as priors in Bayesian nonparametric mixture models is considered. Their…