Compressive Sampling for Remote Control Systems

In remote control, efficient compression or representation of control signals is essential to send them through rate-limited channels. For this purpose, we propose an approach of sparse control signal representation using the compressive sampling technique. The problem of obtaining sparse representation is formulated by cardinality-constrained L2 optimization of the control performance, which is reducible to L1-L2 optimization. The low rate random sampling employed in the proposed method based on the compressive sampling, in addition to the fact that the L1-L2 optimization can be effectively solved by a fast iteration method, enables us to generate the sparse control signal with reduced computational complexity, which is preferable in remote control systems where computation delays seriously degrade the performance. We give a theoretical result for control performance analysis based on the notion of restricted isometry property (RIP). An example is shown to illustrate the effectiveness of the proposed approach via numerical experiments

Sketching for Large-Scale Learning of Mixture Models

Learning parameters from voluminous data can be prohibitive in terms of memory and computational requirements. We propose a "compressive learning" framework where we estimate model parameters from a sketch of the training data. This sketch is a collection of generalized moments of the underlying probability distribution of the data. It can be computed in a single pass on the training set, and is easily computable on streams or distributed datasets. The proposed framework shares similarities with compressive sensing, which aims at drastically reducing the dimension of high-dimensional signals while preserving the ability to reconstruct them. To perform the estimation task, we derive an iterative algorithm analogous to sparse reconstruction algorithms in the context of linear inverse problems. We exemplify our framework with the compressive estimation of a Gaussian Mixture Model (GMM), providing heuristics on the choice of the sketching procedure and theoretical guarantees of reconstruction. We experimentally show on synthetic data that the proposed algorithm yields results comparable to the classical Expectation-Maximization (EM) technique while requiring significantly less memory and fewer computations when the number of database elements is large. We further demonstrate the potential of the approach on real large-scale data (over 10 8 training samples) for the task of model-based speaker verification. Finally, we draw some connections between the proposed framework and approximate Hilbert space embedding of probability distributions using random features. We show that the proposed sketching operator can be seen as an innovative method to design translation-invariant kernels adapted to the analysis of GMMs. We also use this theoretical framework to derive information preservation guarantees, in the spirit of infinite-dimensional compressive sensing