Characterizing coherence, correcting incoherence

Lower previsions defined on a finite set of gambles can be looked at as points in a finite-dimensional real vector space. Within that vector space, the sets of sure loss avoiding and coherent lower previsions form convex polyhedra. We present procedures for obtaining characterizations of these polyhedra in terms of a minimal, finite number of linear constraints. As compared to the previously known procedure, these procedures are more efficient and much more straightforward. Next, we take a look at a procedure for correcting incoherent lower previsions based on pointwise dominance. This procedure can be formulated as a multi-objective linear program, and the availability of the finite characterizations provide an avenue for making these programs computationally feasible

Characterizing coherence, correcting incoherence

Lower previsions defined on a finite set of gambles can be looked at as points in a finite-dimensional real vector space. Within that vector space, the sets of sure loss avoiding and coherent lower previsions form convex polyhedra. We present procedures for obtaining characterizations of these polyhedra in terms of a minimal, finite number of linear constraints. As compared to the previously known procedure, these procedures are more efficient and much more straightforward. Next, we take a look at a procedure for correcting incoherent lower previsions based on pointwise dominance. This procedure can be formulated as a multi-objective linear program, and the availability of the finite characterizations provide an avenue for making these programs computationally feasible

Characterizing Coherence, Correcting Incoherence

Abstract Lower previsions defined on a finite set of gambles can be looked at as points in a finite-dimensional real vector space. Within that vector space, the sets of sure loss avoiding and coherent lower previsions form convex polyhedra. We present procedures for obtaining characterizations of these polyhedra in terms of a minimal, finite number of linear constraints. As compared to the previously known procedure, these procedures are more efficient and much more straightforward. Next, we take a look at a procedure for correcting incoherent lower previsions based on pointwise dominance. This procedure can be formulated as a multi-objective linear program, and the availability of the finite characterizations provide an avenue for making these programs computationally feasible

Block-Sparse Recovery via Convex Optimization

Given a dictionary that consists of multiple blocks and a signal that lives in the range space of only a few blocks, we study the problem of finding a block-sparse representation of the signal, i.e., a representation that uses the minimum number of blocks. Motivated by signal/image processing and computer vision applications, such as face recognition, we consider the block-sparse recovery problem in the case where the number of atoms in each block is arbitrary, possibly much larger than the dimension of the underlying subspace. To find a block-sparse representation of a signal, we propose two classes of non-convex optimization programs, which aim to minimize the number of nonzero coefficient blocks and the number of nonzero reconstructed vectors from the blocks, respectively. Since both classes of problems are NP-hard, we propose convex relaxations and derive conditions under which each class of the convex programs is equivalent to the original non-convex formulation. Our conditions depend on the notions of mutual and cumulative subspace coherence of a dictionary, which are natural generalizations of existing notions of mutual and cumulative coherence. We evaluate the performance of the proposed convex programs through simulations as well as real experiments on face recognition. We show that treating the face recognition problem as a block-sparse recovery problem improves the state-of-the-art results by 10% with only 25% of the training data.Comment: IEEE Transactions on Signal Processin

A Unified Measure of Audio System Fidelity

A new technique to qualitatively measure distortion in dynamically controlled audio systems using non-stationary noise sequences is explored and compared to traditional methods based upon stationary test signals. This technique can easily be adapted to give a qualitative measure of distortion as a function of the perceived Sound Pressure Level (SPL)

A Unified Measure of Audio System Fidelity

A new technique to qualitatively measure distortion in dynamically controlled audio systems using non-stationary noise sequences is explored and compared to traditional methods based upon stationary test signals. This technique can easily be adapted to give a qualitative measure of distortion as a function of the perceived Sound Pressure Level (SPL)