相关论文: Inverting Random Functions III: Discrete MLE Revis…

The MPE (Most Probable Explanation) query plays an important role in probabilistic inference. MPE solution algorithms for probabilistic relational models essentially adapt existing belief assessment method, replacing summation with…

We introduce a concept for random tilings which, comprising the conventional one, is also applicable to tiling ensembles without height representation. In particular, we focus on the random tiling entropy as a function of the tile…

The asymptotic normality of the maximum likelihood estimator (MLE) under regularity conditions is a cornerstone of statistical theory. In this paper, we give explicit upper bounds on the distributional distance between the distribution of…

Parametric density estimation, for example as Gaussian distribution, is the base of the field of statistics. Machine learning requires inexpensive estimation of much more complex densities, and the basic approach is relatively costly…

We apply the techniques of stochastic integration with respect to fractional Brownian motion and the theory of regularity and supremum estimation for stochastic processes to study the maximum likelihood estimator (MLE) for the drift…

High-throughput technologies such as next generation sequencing allow biologists to observe cell function with unprecedented resolution, but the resulting datasets are too large and complicated for humans to understand without the aid of…

Distributional regression aims to find the best candidate in a given parametric family of conditional distributions to model a given dataset. As each candidate in the distribution family can be identified by the corresponding distribution…

Machine learning (ML) has been widely used in the literature to automate software engineering tasks. However, ML outcomes may be sensitive to randomization in data sampling mechanisms and learning procedures. To understand whether and how…

Machine learning (ML) is rapidly transforming the way molecular dynamics simulations are performed and analyzed, from materials modeling to studies of protein folding and function. ML algorithms are often employed to learn low-dimensional…

Large Language Models (LLMs) have recently been successfully applied to regression tasks -- such as time series forecasting and tabular prediction -- by leveraging their in-context learning abilities. However, their autoregressive decoding…

As a popular meta-learning approach, the model-agnostic meta-learning (MAML) algorithm has been widely used due to its simplicity and effectiveness. However, the convergence of the general multi-step MAML still remains unexplored. In this…

We consider a broadcasting problem on a tree where a binary digit (e.g., a spin or a nucleotide's purine/pyrimidine type) is propagated from the root to the leaves through symmetric noisy channels on the edges that randomly flip the state…

Deep latent variable models (DLVMs) combine the approximation abilities of deep neural networks and the statistical foundations of generative models. Variational methods are commonly used for inference; however, the exact likelihood of…

We consider the functional inverse of the Gamma function in the complex plane, where it is multi-valued, and define a set of suitable branches by proposing a natural extension from the real case.

For a (possibly partial) Boolean function $f\colon\{0,1\}^n\to\{0,1\}$ as well as a query complexity measure $M$ which maps Boolean functions to real numbers, define the composition limit of $M$ on $f$ by $M^*(f)=\lim_{k\to\infty}…

The restricted maximum likelihood (REML) estimator of the dispersion matrix for random coefficient models is rewritten in terms of the sufficient statistics of the individual regressions.

This study focuses on the estimation of the Emax dose-response model, a widely utilized framework in clinical trials, agriculture, and environmental experiments. Existing challenges in obtaining maximum likelihood estimates (MLE) for model…

This paper deals with nonparametric maximum likelihood estimation for Gaussian locally stationary processes. Our nonparametric MLE is constructed by minimizing a frequency domain likelihood over a class of functions. The asymptotic behavior…

We provide lower error bounds for randomized algorithms that approximate integrals of functions depending on an unrestricted or even infinite number of variables. More precisely, we consider the infinite-dimensional integration problem on…

The random integral mappings (some type of functionals of L\'evy processes) are continuous homomorphisms between convolution subsemigroups of the semigroup of all infinitely divisible measures. Compositions of those random integrals…