Joint Problems in Learning Multiple Dynamical Systems

Clustering of time series is a well-studied problem, with applications ranging from quantitative, personalized models of metabolism obtained from metabolite concentrations to state discrimination in quantum information theory. We consider a variant, where given a set of trajectories and a number of parts, we jointly partition the set of trajectories and learn linear dynamical system (LDS) models for each part, so as to minimize the maximum error across all the models. We present globally convergent methods and EM heuristics, accompanied by promising computational results.

Distributed Evolution Strategies for Black-box Stochastic Optimization

This work concerns the evolutionary approaches to distributed stochastic black-box optimization, in which each worker can individually solve an approximation of the problem with nature-inspired algorithms. We propose a distributed evolution strategy (DES) algorithm grounded on a proper modification to evolution strategies, a family of classic evolutionary algorithms, as well as a careful combination with existing distributed frameworks. On smooth and nonconvex landscapes, DES has a convergence rate competitive to existing zeroth-order methods, and can exploit the sparsity, if applicable, to match the rate of first-order methods. The DES method uses a Gaussian probability model to guide the search and avoids the numerical issue resulted from finite-difference techniques in existing zeroth-order methods. The DES method is also fully adaptive to the problem landscape, as its convergence is guaranteed with any parameter setting. We further propose two alternative sampling schemes which significantly improve the sampling efficiency while leading to similar performance. Simulation studies on several machine learning problems suggest that the proposed methods show much promise in reducing the convergence time and improving the robustness to parameter settings.

MMES: Mixture Model based Evolution Strategy for Large-Scale Optimization

This work provides an efficient sampling method for the covariance matrix adaptation evolution strategy (CMA-ES) in large-scale settings. In contract to the Gaussian sampling in CMA-ES, the proposed method generates mutation vectors from a mixture model, which facilitates exploiting the rich variable correlations of the problem landscape within a limited time budget. We analyze the probability distribution of this mixture model and show that it approximates the Gaussian distribution of CMA-ES with a controllable accuracy. We use this sampling method, coupled with a novel method for mutation strength adaptation, to formulate the mixture model based evolution strategy (MMES) -- a CMA-ES variant for large-scale optimization. The numerical simulations show that, while significantly reducing the time complexity of CMA-ES, MMES preserves the rotational invariance, is scalable to high dimensional problems, and is competitive against the state-of-the-arts in performing global optimization.

A Decentralized Federated Learning Framework via Committee Mechanism with Convergence Guarantee

Federated learning allows multiple participants to collaboratively train an efficient model without exposing data privacy. However, this distributed machine learning training method is prone to attacks from Byzantine clients, which interfere with the training of the global model by modifying the model or uploading the false gradient. In this paper, we propose a novel serverless federated learning framework Committee Mechanism based Federated Learning (CMFL), which can ensure the robustness of the algorithm with convergence guarantee. In CMFL, a committee system is set up to screen the uploaded local gradients. The committee system selects the local gradients rated by the elected members for the aggregation procedure through the selection strategy, and replaces the committee member through the election strategy. Based on the different considerations of model performance and defense, two opposite selection strategies are designed for the sake of both accuracy and robustness. Extensive experiments illustrate that CMFL achieves faster convergence and better accuracy than the typical Federated Learning, in the meanwhile obtaining better robustness than the traditional Byzantine-tolerant algorithms, in the manner of a decentralized approach. In addition, we theoretically analyze and prove the convergence of CMFL under different election and selection strategies, which coincides with the experimental results.

Blind Inverse Gamma Correction with Maximized Differential Entropy

Unwanted nonlinear gamma distortion frequently occurs in a great diversity of images during the procedures of image acquisition, processing, and/or display. And the gamma distortion often varies with capture setup change and luminance variation. Blind inverse gamma correction, which automatically determines a proper restoration gamma value from a given image, is of paramount importance to attenuate the distortion. For blind inverse gamma correction, an adaptive gamma transformation method (AGT-ME) is proposed directly from a maximized differential entropy model. And the corresponding optimization has a mathematical concise closed-form solution, resulting in efficient implementation and accurate gamma restoration of AGT-ME. Considering the human eye has a non-linear perception sensitivity, a modified version AGT-ME-VISUAL is also proposed to achieve better visual performance. Tested on variable datasets, AGT-ME could obtain an accurate estimation of a large range of gamma distortion (0.1 to 3.0), outperforming the state-of-the-art methods. Besides, the proposed AGT-ME and AGT-ME-VISUAL were applied to three typical applications, including automatic gamma adjustment, natural/medical image contrast enhancement, and fringe projection profilometry image restoration. Furthermore, the AGT-ME/ AGT-ME-VISUAL is general and can be seamlessly extended to the masked image, multi-channel (color or spectrum) image, or multi-frame video, and free of the arbitrary tuning parameter. Besides, the corresponding Python code (https://github.com/yongleex/AGT-ME) is also provided for interested users.