Related papers: Error analysis of a compositional score-based algo…
This paper proposes a novel joint channel-estimation and source-detection algorithm using successive interference cancellation (SIC)-aided generative score-based diffusion models. Prior work in this area focuses on massive MIMO scenarios,…
Generating synthetic datasets that accurately reflect real-world observational data is critical for evaluating causal estimators, but it remains a challenging task. Existing generative methods offer a solution by producing synthetic…
Flagship near-future surveys targeting $10^8-10^9$ galaxies across cosmic time will soon reveal the processes of galaxy assembly in unprecedented resolution. This creates an immediate computational challenge on effective analyses of the…
Through an uncertainty quantification (UQ) perspective, we show that score-based generative models (SGMs) are provably robust to the multiple sources of error in practical implementation. Our primary tool is the Wasserstein uncertainty…
We consider the problem of statistical inference for a class of partially-observed diffusion processes, with discretely-observed data and finite-dimensional parameters. We construct unbiased estimators of the score function, i.e. the…
An energy efficient use of large scale sensor networks necessitates activating a subset of possible sensors for estimation at a fusion center. The problem is inherently combinatorial; to this end, a set of iterative, randomized algorithms…
Simulation-based inference (SBI) is emerging as a new statistical paradigm for addressing complex scientific inference problems. By leveraging the representational power of deep neural networks, SBI can extract the most informative…
While distributed parameter estimation has been extensively studied in the literature, little has been achieved in terms of robust analysis and tuning methods in the presence of disturbances. However, disturbances such as measurement noise…
Despite the remarkable empirical success of score-based diffusion models, their statistical guarantees remain underdeveloped. Existing analyses often provide pessimistic convergence rates that do not reflect the intrinsic low-dimensional…
In this paper, the method of gaps, a technique for deriving closed-form expressions in terms of information measures for the generalization error of supervised machine learning algorithms is introduced. The method relies on the notion of…
This study addresses the problem of discrete signal reconstruction from the perspective of sparse Bayesian learning (SBL). Generally, it is intractable to perform the Bayesian inference with the ideal discretization prior under the SBL…
Sampling-based algorithms are classical approaches to perform Bayesian inference in inverse problems. They provide estimators with the associated credibility intervals to quantify the uncertainty on the estimators. Although these methods…
We propose generalized resubstitution error estimators for regression, a broad family of estimators, each corresponding to a choice of empirical probability measures and loss function. The usual sum of squares criterion is a special case…
We study the problem of high-dimensional sparse mean estimation in the presence of an $\epsilon$-fraction of adversarial outliers. Prior work obtained sample and computationally efficient algorithms for this task for identity-covariance…
This article addresses the issue of estimating observation parameters (response and error parameters) in inverse problems. The focus is on cases where regularization is introduced in a Bayesian framework and the prior is modeled by a…
A popular quantitative approach to evaluating player performance in sports involves comparing an observed outcome to the expected outcome ignoring player involvement, which is estimated using statistical or machine learning methods. In…
Score-based generative modeling (SGM) has grown to be a hugely successful method for learning to generate samples from complex data distributions such as that of images and audio. It is based on evolving an SDE that transforms white noise…
We study the sparse high-dimensional Gaussian mixture model when the number of clusters is allowed to grow with the sample size. A minimax lower bound for parameter estimation is established, and we show that a constrained maximum…
In array processing, a common problem is to estimate the angles of arrival of $K$ deterministic sources impinging on an array of $M$ antennas, from $N$ observations of the source signal, corrupted by gaussian noise. The problem reduces to…
Score-based diffusion models have emerged as powerful techniques for generating samples from high-dimensional data distributions. These models involve a two-phase process: first, injecting noise to transform the data distribution into a…