Multi-modal distributions are commonly used to model clustered data in statistical learning tasks. In this paper, we consider the Mixed Linear Regression (MLR) problem. We propose an optimal transport-based framework for MLR problems, Wasserstein Mixed Linear Regression (WMLR), which minimizes the Wasserstein distance between the learned and target mixture regression models. Through a model-based duality analysis, WMLR reduces the underlying MLR task to a nonconvex-concave minimax optimization problem, which can be provably solved to find a minimax stationary point by the Gradient Descent Ascent (GDA) algorithm. In the special case of mixtures of two linear regression models, we show that WMLR enjoys global convergence and generalization guarantees. We prove that WMLR's sample complexity grows linearly with the dimension of data. Finally, we discuss the application of WMLR to the federated learning task where the training samples are collected by multiple agents in a network. Unlike the Expectation Maximization algorithm, WMLR directly extends to the distributed, federated learning setting. We support our theoretical results through several numerical experiments, which highlight our framework's ability to handle the federated learning setting with mixture models.

Dependent Dirichlet processes (DDP) have been widely applied to model data from distributions over collections of measures which are correlated in some way. On the other hand, in recent years, increasing research efforts in machine learning and data mining have been dedicated to dealing with data involving interactions from two or more factors. However, few researchers have addressed the heterogeneous relationship in data brought by modulation of multiple factors using techniques of DDP. In this paper, we propose a novel technique, MultiLinear Dirichlet Processes (MLDP), to constructing DDPs by combining DP with a state-of-the-art factor analysis technique, multilinear factor analyzers (MLFA). We have evaluated MLDP on real-word data sets for different applications and have achieved state-of-the-art performance. Dependent Dirichlet processes (DDP) have been widely applied to model data from distributions over collections of measures which are correlated in some way. To introduce dependency into DDP, various techniques have been developed via correlating through components of atomic measures, such as atom sizes [8], [11], [23] and atom locations [6], [10], [28], sampling from a DP with random distributions as atoms [24], operating on underlying compound Poisson processes [18], regulating by Lévy Copulas [16], or constructing those measures through a mixture of several independent measures drawn from DPs [12], [15], [19], [20].

Self-supervised learning (SSL) of energy based models has an intuitive relation to equilibrium thermodynamics because the softmax layer, mapping energies to probabilities, is a Gibbs distribution. However, in what way SSL is a thermodynamic process? We show that some SSL paradigms behave as a thermodynamic composite system formed by representations and self-labels in contact with a nonequilibrium reservoir. Moreover, this system is subjected to usual thermodynamic cycles, such as adiabatic expansion and isochoric heating, resulting in a generalized Gibbs ensemble (GGE). In this picture, we show that learning is seen as a demon that operates in cycles using feedback measurements to extract negative work from the system. As applications, we examine some SSL algorithms using this idea.

This paper addresses unsupervised person re-identification (Re-ID) using multi-label prediction and classification based on graph-structural insight. Our method extracts features from person images and produces a graph that consists of the features and a pairwise similarity of them as nodes and edges, respectively. Based on the graph, the proposed graph structure based multi-label prediction (GSMLP) method predicts multi-labels by considering the pairwise similarity and the adjacency node distribution of each node. The multi-labels created by GSMLP are applied to the proposed selective multi-label classification (SMLC) loss. SMLC integrates a hard-sample mining scheme and a multi-label classification. The proposed GSMLP and SMLC boost the performance of unsupervised person Re-ID without any pre-labelled dataset. Experimental results justify the superiority of the proposed method in unsupervised person Re-ID by producing state-of-the-art performance. The source code for this paper is publicly available on 'https://github.com/uknownpioneer/GSMLP-SMLC.git'.

Mobile Augmented Reality (MAR) integrates computer-generated virtual objects with physical environments for mobile devices. MAR systems enable users to interact with MAR devices, such as smartphones and head-worn wearables, and performs seamless transitions from the physical world to a mixed world with digital entities. These MAR systems support user experiences by using MAR devices to provide universal accessibility to digital contents. Over the past 20 years, a number of MAR systems have been developed, however, the studies and design of MAR frameworks have not yet been systematically reviewed from the perspective of user-centric design. This article presents the first effort of surveying existing MAR frameworks (count: 37) and further discusses the latest studies on MAR through a top-down approach: 1) MAR applications; 2) MAR visualisation techniques adaptive to user mobility and contexts; 3) systematic evaluation of MAR frameworks including supported platforms and corresponding features such as tracking, feature extraction plus sensing capabilities; and 4) underlying machine learning approaches supporting intelligent operations within MAR systems. Finally, we summarise the development of emerging research fields, current state-of-the-art, and discuss the important open challenges and possible theoretical and technical directions. This survey aims to benefit both researchers and MAR system developers alike.

We present an online multi-task learning approach for adaptive nonlinear control, which we call Online Meta-Adaptive Control (OMAC). The goal is to control a nonlinear system subject to adversarial disturbance and unknown $\textit{environment-dependent}$ nonlinear dynamics, under the assumption that the environment-dependent dynamics can be well captured with some shared representation. Our approach is motivated by robot control, where a robotic system encounters a sequence of new environmental conditions that it must quickly adapt to. A key emphasis is to integrate online representation learning with established methods from control theory, in order to arrive at a unified framework that yields both control-theoretic and learning-theoretic guarantees. We provide instantiations of our approach under varying conditions, leading to the first non-asymptotic end-to-end convergence guarantee for multi-task adaptive nonlinear control. OMAC can also be integrated with deep representation learning. Experiments show that OMAC significantly outperforms conventional adaptive control approaches which do not learn the shared representation.

With the surge in the number of hyperparameters and training times of modern machine learning models, hyperparameter tuning is becoming increasingly expensive. Although methods have been proposed to speed up tuning via knowledge transfer, they typically require the final performance of hyperparameters and do not focus on low-fidelity information. Nevertheless, this common practice is suboptimal and can incur an unnecessary use of resources. It is more cost-efficient to instead leverage the low-fidelity tuning observations to measure inter-task similarity and transfer knowledge from existing to new tasks accordingly. However, performing multi-fidelity tuning comes with its own challenges in the transfer setting: the noise in the additional observations and the need for performance forecasting. Therefore, we conduct a thorough analysis of the multi-task multi-fidelity Bayesian optimization framework, which leads to the best instantiation--amortized auto-tuning (AT2). We further present an offline-computed 27-task hyperparameter recommendation (HyperRec) database to serve the community. Extensive experiments on HyperRec and other real-world databases illustrate the effectiveness of our AT2 method.

In a binary classification problem where the goal is to fit an accurate predictor, the presence of corrupted labels in the training data set may create an additional challenge. However, in settings where likelihood maximization is poorly behaved-for example, if positive and negative labels are perfectly separable-then a small fraction of corrupted labels can improve performance by ensuring robustness. In this work, we establish that in such settings, corruption acts as a form of regularization, and we compute precise upper bounds on estimation error in the presence of corruptions. Our results suggest that the presence of corrupted data points is beneficial only up to a small fraction of the total sample, scaling with the square root of the sample size.

Strong correlations between explanatory variables are problematic for high-dimensional regularized regression methods. Due to the violation of the Irrepresentable Condition, the popular LASSO method may suffer from false inclusions of inactive variables. In this paper, we propose pre-processing with orthogonal decompositions (PROD) for the explanatory variables in high-dimensional regressions. The PROD procedure is constructed based upon a generic orthogonal decomposition of the design matrix. We demonstrate by two concrete cases that the PROD approach can be effectively constructed for improving the performance of high-dimensional penalized regression. Our theoretical analysis reveals their properties and benefits for high-dimensional penalized linear regression with LASSO.

Multi-task learning (MTL) aims to improve the generalization of several related tasks by learning them jointly. As a comparison, in addition to the joint training scheme, modern meta-learning allows unseen tasks with limited labels during the test phase, in the hope of fast adaptation over them. Despite the subtle difference between MTL and meta-learning in the problem formulation, both learning paradigms share the same insight that the shared structure between existing training tasks could lead to better generalization and adaptation. In this paper, we take one important step further to understand the close connection between these two learning paradigms, through both theoretical analysis and empirical investigation. Theoretically, we first demonstrate that MTL shares the same optimization formulation with a class of gradient-based meta-learning (GBML) algorithms. We then prove that for over-parameterized neural networks with sufficient depth, the learned predictive functions of MTL and GBML are close. In particular, this result implies that the predictions given by these two models are similar over the same unseen task. Empirically, we corroborate our theoretical findings by showing that, with proper implementation, MTL is competitive against state-of-the-art GBML algorithms on a set of few-shot image classification benchmarks. Since existing GBML algorithms often involve costly second-order bi-level optimization, our first-order MTL method is an order of magnitude faster on large-scale datasets such as mini-ImageNet. We believe this work could help bridge the gap between these two learning paradigms, and provide a computationally efficient alternative to GBML that also supports fast task adaptation.