Related papers: Random Function Priors for Correlation Modeling

Recent progress in deterministic prompt learning has become a promising alternative to various downstream vision tasks, enabling models to learn powerful visual representations with the help of pre-trained vision-language models. However,…

Sentence embedding is one of the most fundamental tasks in Natural Language Processing and plays an important role in various tasks. The recent breakthrough in sentence embedding is achieved by pre-trained language models (PLMs). Despite…

Kinetic parameters such as the turnover number ($k_{cat}$) and Michaelis constant ($K_{\mathrm{M}}$) are essential for modelling enzymatic activity but experimental data remains limited in scale and diversity. Previous methods for…

We obtain results on the asymptotic equidistribution of the pre-images of linear subspaces for sequences of rational mappings between projective spaces. As an application to complex dynamics, we consider the iterates $P_k$ of a rational…

We introduce a novel class of sample-based explanations we term high-dimensional representers, that can be used to explain the predictions of a regularized high-dimensional model in terms of importance weights for each of the training…

Regression models, in which the observed features $X \in \R^p$ and the response $Y \in \R$ depend, jointly, on a lower dimensional, unobserved, latent vector $Z \in \R^K$, with $K< p$, are popular in a large array of applications, and…

Word embeddings have been found to capture a surprisingly rich amount of syntactic and semantic knowledge. However, it is not yet sufficiently well-understood how the relational knowledge that is implicitly encoded in word embeddings can be…

The generalization gap of a classifier is related to the complexity of the set of functions among which the classifier is chosen. We study a family of low-complexity classifiers consisting of thresholding a random one-dimensional feature.…

We give an asymptotic formula for correlations \[ \sum_{n\le x}f_1(P_1(n))f_2(P_2(n))\cdot \dots \cdot f_m(P_m(n))\] where $f\dots,f_m$ are bounded "pretentious" multiplicative functions, under certain natural hypotheses. We then deduce…

Bayesian variable selection has gained much empirical success recently in a variety of applications when the number $K$ of explanatory variables $(x_1,...,x_K)$ is possibly much larger than the sample size $n$. For generalized linear…

Generative modeling provides a powerful framework for learning data distributions. These models initially relied on probabilistic methods such as Gaussian Processes (GP) for uncertainty-aware predictions and shifted towards larger trainable…

The quality of data representation in deep learning methods is directly related to the prior model imposed on the representations; however, generally used fixed priors are not capable of adjusting to the context in the data. To address this…

Particularly in low-data regimes, an outstanding challenge in machine learning is developing principled techniques for augmenting our models with suitable priors. This is to encourage them to learn in ways that are compatible with our…

We present a deep transformation model for probabilistic regression. Deep learning is known for outstandingly accurate predictions on complex data but in regression tasks, it is predominantly used to just predict a single number. This…

Paired comparison data considered in this paper originate from the comparison of a large number N of individuals in couples. The dataset is a collection of results of contests between two individuals when each of them has faced n opponents,…

This paper develops a general theory on rates of convergence of penalized spline estimators for function estimation when the likelihood functional is concave in candidate functions, where the likelihood is interpreted in a broad sense that…

In this paper, we introduce a probabilistic model for learning nonnegative matrix factorization (NMF) that is commonly used for predicting missing values and finding hidden patterns in the data, in which the matrix factors are latent…

We give a new large deviation inequality for sums of random variables of the form $Z_k = f(X_k,X_t)$ for $k,t\in \mathbb{N}$, $t$ fixed, where the underlying process $X$ is $\beta$-mixing. The inequality can be used to derive concentration…

A very elementary model of a single positive hermitian random matrix coupled to an external matrix is defined and studied. Expanding the exact effective action around its classical solution leads to the ``quantum Penner action'', from which…

We investigate the relationship between the geometry of token embeddings and their role in the next token prediction within transformer models. An important aspect of this connection uses the notion of empirical measure, which encodes the…