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Sparse structure learning in high-dimensional Gaussian graphical models is an important problem in multivariate statistical signal processing; since the sparsity pattern naturally encodes the conditional independence relationship among…
We establish non-asymptotic efficiency guarantees for tensor decomposition-based inference in count data models. Under a Poisson framework, we consider two related goals: (i) parametric inference, the estimation of the full distributional…
Approximate message passing (AMP) is an effective iterative sparse recovery algorithm for linear system models. Its performance is characterized by the state evolution (SE) which is a simple scalar recursion. However, depending on a…
Approximate message passing algorithm enjoyed considerable attention in the last decade. In this paper we introduce a variant of the AMP algorithm that takes into account glassy nature of the system under consideration. We coin this…
In order to reduce hardware complexity and power consumption, massive multiple-input multiple-output (MIMO) systems employ low-resolution analog-to-digital converters (ADCs) to acquire quantized measurements $\boldsymbol y$. This poses new…
Approximate message passing (AMP) is an efficient iterative signal recovery algorithm for compressed sensing (CS). For sensing matrices with independent and identically distributed (i.i.d.) Gaussian entries, the behavior of AMP can be…
In compressed sensing one measures sparse signals directly in a compressed form via a linear transform and then reconstructs the original signal. However, it is often the case that the linear transform itself is known only approximately, a…
In variational inference, the benefits of Bayesian models rely on accurately capturing the true posterior distribution. We propose using neural samplers that specify implicit distributions, which are well-suited for approximating complex…
Deep learning has gained great popularity due to its widespread success on many inference problems. We consider the application of deep learning to the sparse linear inverse problem, where one seeks to recover a sparse signal from a few…
We propose regularized approximate message passing (RAMP), a low-complexity algorithm for discrete signal detection in overloaded multiple-input multiple-output (MIMO) systems where the number of transmit antennas exceeds the number of…
Multi-modal learning aims to enhance performance by unifying models from various modalities but often faces the "modality imbalance" problem in real data, leading to a bias towards dominant modalities and neglecting others, thereby limiting…
The performance of Maximum a posteriori (MAP) estimation is studied analytically for binary symmetric multi-channel Hidden Markov processes. We reduce the estimation problem to a 1D Ising spin model and define order parameters that…
Cross-modal embeddings, between textual and visual modalities, aim to organise multimodal instances by their semantic correlations. State-of-the-art approaches use maximum-margin methods, based on the hinge-loss, to enforce a constant…
In this paper, we propose a deep learning aided list approximate message passing (AMP) algorithm to further improve the user identification performance in massive machine type communications. A neural network is employed to identify a…
We propose an orthogonal approximate message passing (OAMP) algorithm for signal estimation in the rectangular spiked matrix model with general rotationally invariant (RI) noise. We establish a rigorous state evolution that precisely…
Factorizing low-rank matrices is a problem with many applications in machine learning and statistics, ranging from sparse PCA to community detection and sub-matrix localization. For probabilistic models in the Bayes optimal setting, general…
We address the problem of estimating a high-dimensional matrix from linear measurements, with a focus on designing optimal rank-adaptive algorithms. These algorithms infer the matrix by estimating its singular values and the corresponding…
The main difficulty that arises in the analysis of most machine learning algorithms is to handle, analytically and numerically, a large number of interacting random variables. In this Ph.D manuscript, we revisit an approach based on the…
State-of-the-art neural network language models (NNLMs) represented by long short term memory recurrent neural networks (LSTM-RNNs) and Transformers are becoming highly complex. They are prone to overfitting and poor generalization when…
We study the performance of a Bayesian statistician who estimates a rank-one signal corrupted by non-symmetric rotationally invariant noise with a generic distribution of singular values. As the signal-to-noise ratio and the noise structure…