Related papers: Negatively Biased Relevant Subsets Induced by the …
Bayesian inverse problem on an infinite dimensional separable Hilbert space with the whole state observed is well posed when the prior state distribution is a Gaussian probability measure and the data error covariance is a cylindric…
We reconsider the constraints on Universal Extra Dimensions (UED) models arising from precision electroweak data. We take into account the subleading contributions from new physics (expressed in terms of the X,Y ... variables), as well as…
We consider fully connected and feedforward deep neural networks with dependent and possibly heavy-tailed weights, as introduced in [26], to address limitations of the standard Gaussian prior. It has been proved in [26] that, as the number…
For several styles of fidelity constraints -- guaranteed distortion, conditional excess distortion, excess distortion -- we show mutual information upper bounds on the minimum expected description length needed to represent a random…
Being able to reliably assess not only the \emph{accuracy} but also the \emph{uncertainty} of models' predictions is an important endeavour in modern machine learning. Even if the model generating the data and labels is known, computing the…
Contrastive learning relies on an assumption that positive pairs contain related views, e.g., patches of an image or co-occurring multimodal signals of a video, that share certain underlying information about an instance. But what if this…
The investigation of the volume, surface area, and other geometric properties of sections of convex bodies, and in particular cubes, has a long history and a rich literature. However, much less is known when the cube has a volume…
With Bayesian statistics, we investigate the full parameter space of the constrained "next-to-minimal" supersymmetric Standard Model (CNMSSM) with naturalness priors, which were derived in a previous work. In the past, most Bayesian…
We establish strong duality relations for functional two-step compositional risk-constrained learning problems with multiple nonconvex loss functions and/or learning constraints, regardless of nonconvexity and under a minimal set of…
Adversarial vulnerability in vision and hallucination in large language models are conventionally viewed as separate problems, each addressed with modality-specific patches. This study first reveals that they share a common geometric…
The problem of establishing out-of-sample bounds for the values of an unkonwn ground-truth function is considered. Kernels and their associated Hilbert spaces are the main formalism employed herein along with an observational model where…
Concentration inequalities form an essential toolkit in the study of high dimensional (HD) statistical methods. Most of the relevant statistics literature in this regard is based on sub-Gaussian or sub-exponential tail assumptions. In this…
We study the problem of nonparametric regression when the regressor is endogenous, which is an important nonparametric instrumental variables (NPIV) regression in econometrics and a difficult ill-posed inverse problem with unknown operator…
The constrained Cramer-Rao bound (CCRB) is a lower bound on the mean-squared-error (MSE) of estimators that satisfy some unbiasedness conditions. Although the CCRB unbiasedness conditions are satisfied asymptotically by the constrained…
This paper addresses the estimation of signals with sublinear sparsity sent over the additive white Gaussian noise channel. This fundamental problem arises in designing denoisers used in message-passing algorithms for sublinear sparsity.…
We establish some new non-asymptotical lower bounds for deviation of regular unbiased estimation of unknown parameter from its true value in different norms, alike the classical Rao-Kramer's inequality. We show that if the new norm is…
With surge of available but unlabeled data, Positive Unlabeled (PU) learning is becoming a thriving challenge. This work deals with this demanding task for which recent GAN-based PU approaches have demonstrated promising results. Generative…
Significance testing based on p-values has been implicated in the reproducibility crisis in scientific research, with one of the proposals being to eliminate them in favor of Bayesian analyses. Defenders of the p-values have countered that…
Secure distributed data compression in the presence of an eavesdropper is explored. Two correlated sources that need to be reliably transmitted to a legitimate receiver are available at separate encoders. Noise-free, limited rate links from…
We present a new upper limit of sum m_{\nu} eV < 0.28 (95% CL) on the sum of the neutrino masses assuming a flat LCDM cosmology. This relaxes slightly to sum m_{\nu} < 0.34 and sum m_{\nu} < 0.47 when quasi non-linear scales are removed and…