Sharif Digital Repository

A Bernoulli Mixture Model (BMM) is a finite mixture of random binary vectors with independent dimensions. The problem of clustering BMM data arises in a variety of real-world applications, ranging from population genetics to activity analysis in social networks. In this paper, we analyze the clusterability of BMMs from a theoretical perspective, when the number of clusters is unknown. In particular, we stipulate a set of conditions on the sample complexity and dimension of the model in order to guarantee the Probably Approximately Correct (PAC)-clusterability of a dataset. To the best of our knowledge, these findings are the first non-asymptotic bounds on the sample complexity of learning or... 

We study the sample complexity of learning a high-dimensional simplex from a set of points uniformly sampled from its interior. Learning of simplices is a long studied problem in computer science and has applications in computational biology and remote sensing, mostly under the name of “spectral unmixing.” We theoretically show that a sufficient sample complexity for reliable learning of a K-dimensional simplex up to a total-variation error of ε is O(Kε2 log Kε ), which yields a substantial improvement over existing bounds. Based on our new theoretical framework, we also propose a heuristic approach for the inference of simplices. Experimental results on synthetic and real-world datasets... 

This work is about the total variation (TV) minimization which is used for recovering gradient-sparse signals from compressed measurements. Recent studies indicate that TV minimization exhibits a phase transition behavior from failure to success as the number of measurements increases. In fact, in large dimensions, TV minimization succeeds in recovering the gradient-sparse signal with high probability when the number of measurements exceeds a certain threshold; otherwise, it fails almost certainly. Obtaining a closed-form expression that approximates this threshold is a major challenge in this field and has not been appropriately addressed yet. In this work, we derive a tight lower-bound on... 

This letter considers the use of total variation (TV) minimization in the recovery of a given gradient sparse vector from Gaussian linear measurements. It has been shown in recent studies that there exists a sharp phase transition behavior in TV minimization for the number of measurements necessary to recover the signal in asymptotic regimes. The phase-transition curve specifies the boundary of success and failure of TV minimization for large number of measurements. It is a challenging task to obtain a theoretical bound that reflects this curve. In this letter, we present a novel upper bound that suitably approximates this curve and is asymptotically sharp. Numerical results show that our... 

One of the most studied problems in machine learning is finding reasonable constraints that guarantee the generalization of a learning algorithm. These constraints are usually expressed as some simplicity assumptions on the target. For instance, in the Vapnik–Chervonenkis (VC) theory the space of possible hypotheses is considered to have a limited VC dimension One way to formulate the simplicity assumption is via information theoretic concepts. In this paper, the constraint on the entropy H(X) of the input variable X is studied as a simplicity assumption. It is proven that the sample complexity to achieve an ∊-δ Probably Approximately Correct (PAC) hypothesis is bounded by [Formula... 

This article proposes a compressed-domain signal processing (CSP) multiple-input multiple-output (MIMO) radar, a MIMO radar approach that achieves substantial sample complexity reduction by exploiting the idea of CSP. CSP MIMO radar involves two levels of data compression followed by target detection at the compressed domain. First, compressive sensing is applied at the receive antennas, followed by a Capon beamformer, which is designed to suppress clutter. Exploiting the sparse nature of the beamformer output, a second compression is applied to the filtered data. Target detection is subsequently conducted by formulating and solving a hypothesis testing problem at each grid point of the...