相关论文: Exponential Observation Error in Boundary Region

As a class of state-dependent channels, Markov channels have been long studied in information theory for characterizing the feedback capacity and error exponent. This paper studies a more general variant of such channels where the state…

Since its application to systems, emergence has been explained in terms of levels of observation. This approach has led to confusion, contradiction, incoherence and at times mysticism. When the idea of level is replaced by a framework of…

The goal of ordinal embedding is to represent items as points in a low-dimensional Euclidean space given a set of constraints in the form of distance comparisons like "item $i$ is closer to item $j$ than item $k$". Ordinal constraints like…

Particle filtering is a Bayesian inference method and a fundamental tool in state estimation for dynamic systems, but its effectiveness is often limited by the constraints of the initial prior distribution, a phenomenon we define as the…

Capturing interpretable variations has long been one of the goals in disentanglement learning. However, unlike the independence assumption, interpretability has rarely been exploited to encourage disentanglement in the unsupervised setting.…

For better learning, large datasets are often split into small batches and fed sequentially to the predictive model. In this paper, we study such batch decompositions from a probabilistic perspective. We assume that data points (possibly…

We define the local empirical process, based on $n$ i.i.d. random vectors in dimension $d$, in the neighborhood of the boundary of a fixed set. Under natural conditions on the shrinking neighborhood, we show that, for these local empirical…

Evaluating the statistical dimension is a common tool to determine the asymptotic phase transition in compressed sensing problems with Gaussian ensemble. Unfortunately, the exact evaluation of the statistical dimension is very difficult and…

Predictive algorithms inform consequential decisions in settings with selective labels: outcomes are observed only for units selected by past decision makers. This creates an identification problem under unobserved confounding -- when…

Distributed learning facilitates the scaling-up of data processing by distributing the computational burden over several nodes. Despite the vast interest in distributed learning, generalization performance of such approaches is not well…

Latent space Energy-Based Models (EBMs), also known as energy-based priors, have drawn growing interests in generative modeling. Fueled by its flexibility in the formulation and strong modeling power of the latent space, recent works built…

We revisit the problem of estimating the parameters of a partially observed diffusion process, consisting of a hidden state process and an observed process, with a continuous time parameter. The estimation is to be done online, i.e. the…

Expectation Propagation (EP) provides a framework for approximate inference. When the model under consideration is over a latent Gaussian field, with the approximation being Gaussian, we show how these approximations can systematically be…

We revisit the maximum-entropy inference of the state of a finite-level quantum system under linear constraints. The constraints are specified by the expected values of a set of fixed observables. We point out the existence of…

We consider the discrete memoryless asymmetric broadcast channels. We prove that the error probability of decoding tends to one exponentially for rates outside the capacity region and derive an explicit lower bound of this exponent…

Traditional state estimation methods rely on probabilistic assumptions that often collapse epistemic uncertainty into scalar beliefs, risking overconfidence in sparse or adversarial sensing environments. We introduce the Epistemic…

In the presence of unmeasured spatial confounding, spatial models may actually increase (rather than decrease) bias, leading to uncertainty as to how they should be applied in practice. We evaluated spatial modeling approaches through…

Machine learning classifiers often produce probabilistic predictions that are critical for accurate and interpretable decision-making in various domains. The quality of these predictions is generally evaluated with proper losses, such as…

Let I_1,...,I_n be independent but not necessarily identically distributed Bernoulli random variables, and let X_n=\sum_{j=1}^nI_j. For \nu in a bounded region, a local central limit theorem expansion of P(X_n=EX_n+\nu) is developed to any…

Sparse representation over redundant dictionaries constitutes a good model for many classes of signals (e.g., patches of natural images, segments of speech signals, etc.). However, despite its popularity, very little is known about the…