Related papers: Off-the-grid prediction and testing for linear com…
We study the question of extracting a sequence of functions $\{\boldsymbol{f}_i, \boldsymbol{g}_i\}_{i=1}^s$ from observing only the sum of their convolutions, i.e., from $\boldsymbol{y} = \sum_{i=1}^s \boldsymbol{f}_i\ast…
We study filtering of multiscale dynamical systems with model error arising from unresolved smaller scale processes. The analysis assumes continuous-time noisy observations of all components of the slow variables alone. For a linear model…
Out-of-distribution (OOD) detection, crucial for reliable pattern classification, discerns whether a sample originates outside the training distribution. This paper concentrates on the high-dimensional features output by the final…
We investigate the increasingly prominent task of jointly inferring multiple networks from nodal observations. While most joint inference methods assume that observations are available at all nodes, we consider the realistic and more…
A main puzzle of deep networks revolves around the absence of overfitting despite large overparametrization and despite the large capacity demonstrated by zero training error on randomly labeled data. In this note, we show that the dynamics…
This paper considers binary classification of high-dimensional features under a postulated model with a low-dimensional latent Gaussian mixture structure and non-vanishing noise. A generalized least squares estimator is used to estimate the…
We consider the problem of detecting a community of densely connected vertices in a high-dimensional bipartite graph of size $n_1 \times n_2$. Under the null hypothesis, the observed graph is drawn from a bipartite Erd\H{o}s-Renyi…
We consider composite-composite testing problems for the expectation in the Gaussian sequence model where the null hypothesis corresponds to a convex subset $\mathcal{C}$ of $\mathbb{R}^d$. We adopt a minimax point of view and our primary…
Outlier detection has gained increasing interest in recent years, due to newly emerging technologies and the huge amount of high-dimensional data that are now available. Outlier detection can help practitioners to identify unwanted noise…
The problem of detecting correlations from samples of a high-dimensional Gaussian vector has recently received a lot of attention. In most existing work, detection procedures are provided with a full sample. However, following common wisdom…
We study the problem of signal estimation from non-linear observations when the signal belongs to a low-dimensional set buried in a high-dimensional space. A rough heuristic often used in practice postulates that non-linear observations may…
We consider the high-dimensional inference problem where the signal is a low-rank symmetric matrix which is corrupted by an additive Gaussian noise. Given a probabilistic model for the low-rank matrix, we compute the limit in the large…
We propose an adversarial evaluation framework for sensitive feature inference based on minimum mean-squared error (MMSE) estimation with a finite sample size and linear predictive models. Our approach establishes theoretical lower bounds…
This paper describes computationally efficient approaches and associated theoretical performance guarantees for the detection of known targets and anomalies from few projection measurements of the underlying signals. The proposed approaches…
We propose a greedy variational method for decomposing a non-negative multivariate signal as a weighted sum of Gaussians, which, borrowing the terminology from statistics, we refer to as a Gaussian mixture model. Notably, our method has the…
We propose a methodology for testing linear hypothesis in high-dimensional linear models. The proposed test does not impose any restriction on the size of the model, i.e. model sparsity or the loading vector representing the hypothesis.…
In the standard Gaussian linear measurement model $Y=X\mu_0+\xi \in \mathbb{R}^m$ with a fixed noise level $\sigma>0$, we consider the problem of estimating the unknown signal $\mu_0$ under a convex constraint $\mu_0 \in K$, where $K$ is a…
This paper considers the problem of estimating a periodic function in a continuous time regression model with an additive stationary gaussian noise having unknown correlation function. A general model selection procedure on the basis of…
We consider the problem of estimating the frequency components of a mixture of s complex sinusoids from a random subset of n regularly spaced samples. Unlike previous work in compressed sensing, the frequencies are not assumed to lie on a…
Unlinked regression, in which covariates and responses are observed separately without known correspondence, has recently gained increasing attention. Deconvolution, on the other hand, is a fundamental and challenging problem in…