Related papers: Learning Theory Informed Priors for Bayesian Infer…

Recent Vision-Language Pretrained (VLP) models have become the backbone for many downstream tasks, but they are utilized as frozen model without learning. Prompt learning is a method to improve the pre-trained VLP model by adding a…

Denoising autoencoders (DAEs) have proven useful for unsupervised representation learning, but a thorough theoretical understanding is still lacking of how the input noise influences learning. Here we develop theory for how noise influences…

Variational Auto-Encoders (VAEs) are known to generate blurry and inconsistent samples. One reason for this is the "prior hole" problem. A prior hole refers to regions that have high probability under the VAE's prior but low probability…

In the realm of thermodynamics of apparent horizon, we construct a dark energy (DE) model from 4-parameter generalized entropy of apparent horizon in a spatially non-flat universe. In particular, considering a non-zero spatial curvature of…

The EDE model is one of the promising solutions to the long-standing Hubble tension. This paper investigates the status of several EDE models in light of recent BAO observations from the Dark Energy Spectroscopic Instrument (DESI) and their…

In this work, two different models, one with cosmological constant $\Lambda$, and baryonic and dark matter (with $\omega_{dm} \neq 0$), and the other with an $X$ dark energy (with $\omega_{de} \neq -1$), and baryonic and dark matter (with…

We study non-linear Bayesian inverse problems arising from semilinear partial differential equations (PDEs) that can be transformed into linear Bayesian inverse problems. We are then able to extend the early stopping for Ensemble…

In this article we consider Bayesian inference associated to deep neural networks (DNNs) and in particular, trace-class neural network (TNN) priors which can be preferable to traditional DNNs as (a) they are identifiable and (b) they…

Motivated by the recent baryon acoustic oscillation measurements of DESI DR2 collaboration, this works presents an extended analysis of a cosmological model based on holographic dark energy within the framework of Unimodular Gravity. We…

Most deep latent factor models choose simple priors for simplicity, tractability or not knowing what prior to use. Recent studies show that the choice of the prior may have a profound effect on the expressiveness of the model,especially…

Deterministic neural networks (NNs) are increasingly being deployed in safety critical domains, where calibrated, robust, and efficient measures of uncertainty are crucial. In this paper, we propose a novel method for training non-Bayesian…

In this work, we consider the problem of identifying an unknown linear dynamical system given a finite hypothesis class. In particular, we analyze the effect of the excitation input on the sample complexity of identifying the true system…

The conditional density characterizes the distribution of a response variable $y$ given other predictor $x$, and plays a key role in many statistical tasks, including classification and outlier detection. Although there has been abundant…

We study dark energy through the viewpoints of parametric and nonparametric analyses of late-time cosmological data. We consider four Hubble parameter priors reflecting the Hubble tension and make use of two phenomenological functions,…

Physics-inspired neural networks (NNs), such as Hamiltonian or Lagrangian NNs, dramatically outperform other learned dynamics models by leveraging strong inductive biases. These models, however, are challenging to apply to many real world…

Partial differential equations (PDEs) govern a wide range of physical systems, but solving them efficiently remains a major challenge. The idea of a scientific foundation model (SciFM) is emerging as a promising tool for learning…

When training data is scarce, the incorporation of additional prior knowledge can assist the learning process. While it is common to initialize neural networks with weights that have been pre-trained on other large data sets, pre-training…

We provide a new interpretation for the Bayes factor combination used in the Dark Energy Survey (DES) first year analysis to quantify the tension between the DES and Planck datasets. The ratio quantifies a Bayesian confidence in our ability…

In this paper, we derive a Bayesian model order selection rule by using the exponentially embedded family method, termed Bayesian EEF. Unlike many other Bayesian model selection methods, the Bayesian EEF can use vague proper priors and…

Discriminative training techniques define state-of-the-art performance for automatic speech recognition systems. However, they are inherently prone to overfitting, leading to poor generalization performance when using limited training data.…