In this paper, we propose a variance reduction approach for Markov chains based on additive control variates and the minimization of an appropriate estimate for the asymptotic variance. We focus on the particular case when control variates are represented as deep neural networks. We derive the optimal convergence rate of the asymptotic variance under various ergodicity assumptions on the underlying Markov chain. The proposed approach relies upon recent results on the stochastic errors of variance reduction algorithms and function approximation theory.

The difficulty in acquiring a sufficient amount of training data is a major bottleneck for machine learning (ML) based data analytics. Recently, commoditizing ML models has been proposed as an economical and moderate solution to ML-oriented data acquisition. However, existing model marketplaces assume that the broker can access data owners' private training data, which may not be realistic in practice. In this paper, to promote trustworthy data acquisition for ML tasks, we propose FL-Market, a locally private model marketplace that protects privacy not only against model buyers but also against the untrusted broker. FL-Market decouples ML from the need to centrally gather training data on the broker's side using federated learning, an emerging privacy-preserving ML paradigm in which data owners collaboratively train an ML model by uploading local gradients (to be aggregated into a global gradient for model updating). Then, FL-Market enables data owners to locally perturb their gradients by local differential privacy and thus further prevents privacy risks. To drive FL-Market, we propose a deep learning-empowered auction mechanism for intelligently deciding the local gradients' perturbation levels and an optimal aggregation mechanism for aggregating the perturbed gradients. Our auction and aggregation mechanisms can jointly maximize the global gradient's accuracy, which optimizes model buyers' utility. Our experiments verify the effectiveness of the proposed mechanisms.

We introduce novel convergence results for asynchronous iterations that appear in the analysis of parallel and distributed optimization algorithms. The results are simple to apply and give explicit estimates for how the degree of asynchrony impacts the convergence rates of the iterates. Our results shorten, streamline and strengthen existing convergence proofs for several asynchronous optimization methods and allow us to establish convergence guarantees for popular algorithms that were thus far lacking a complete theoretical understanding. Specifically, we use our results to derive better iteration complexity bounds for proximal incremental aggregated gradient methods, to obtain tighter guarantees depending on the average rather than maximum delay for the asynchronous stochastic gradient descent method, to provide less conservative analyses of the speedup conditions for asynchronous block-coordinate implementations of Krasnoselskii-Mann iterations, and to quantify the convergence rates for totally asynchronous iterations under various assumptions on communication delays and update rates.

Deep latent generative models have attracted increasing attention due to the capacity of combining the strengths of deep learning and probabilistic models in an elegant way. The data representations learned with the models are often continuous and dense. However in many applications, sparse representations are expected, such as learning sparse high dimensional embedding of data in an unsupervised setting, and learning multi-labels from thousands of candidate tags in a supervised setting. In some scenarios, there could be further restriction on degree of sparsity: the number of non-zero features of a representation cannot be larger than a pre-defined threshold $L_0$. In this paper we propose a sparse deep latent generative model SDLGM to explicitly model degree of sparsity and thus enable to learn the sparse structure of the data with the quantified sparsity constraint. The resulting sparsity of a representation is not fixed, but fits to the observation itself under the pre-defined restriction. In particular, we introduce to each observation $i$ an auxiliary random variable $L_i$, which models the sparsity of its representation. The sparse representations are then generated with a two-step sampling process via two Gumbel-Softmax distributions. For inference and learning, we develop an amortized variational method based on MC gradient estimator. The resulting sparse representations are differentiable with backpropagation. The experimental evaluation on multiple datasets for unsupervised and supervised learning problems shows the benefits of the proposed method.

Learning models that are robust to distribution shifts is a key concern in the context of their real-life applicability. Invariant Risk Minimization (IRM) is a popular framework that aims to learn robust models from multiple environments. The success of IRM requires an important assumption: the underlying causal mechanisms/features remain invariant across environments. When not satisfied, we show that IRM can over-constrain the predictor and to remedy this, we propose a relaxation via $\textit{partial invariance}$. In this work, we theoretically highlight the sub-optimality of IRM and then demonstrate how learning from a partition of training domains can help improve invariant models. Several experiments, conducted both in linear settings as well as with deep neural networks on tasks over both language and image data, allow us to verify our conclusions.

Studies on benign overfitting provide insights for the success of overparameterized deep learning models. In this work, we examine whether overfitting is truly benign in real-world classification tasks. We start with the observation that a ResNet model overfits benignly on Cifar10 but not benignly on ImageNet. To understand why benign overfitting fails in the ImageNet experiment, we theoretically analyze benign overfitting under a more restrictive setup where the number of parameters is not significantly larger than the number of data points. Under this mild overparameterization setup, our analysis identifies a phase change: unlike in the previous heavy overparameterization settings, benign overfitting can now fail in the presence of label noise. Our analysis explains our empirical observations, and is validated by a set of control experiments with ResNets. Our work highlights the importance of understanding implicit bias in underfitting regimes as a future direction.

Tensor decomposition is widely used in data science and machine learning [1]. For instance, It plays the central roles in signal processing by contribution analysis [2], data compression by converting tensor data to matrix data [3], and data recovery by counting backwards from the matrices to the original tensor data [4]. In many cases, tensor decomposition itself is known to be NP-hard [5]. For this reason, tensor decomposition is often calculated approximately by Bayesian inference. However, its mathematical property is not yet completely clarified because it is one of the singular statistical models. In this paper, we derive its generalization performance in Bayesian inference. Tensor decomposition has mainly two types: Tucker decomposition and CP decomposition.

Machine learning is increasingly used to discover diagnostic and prognostic biomarkers from high-dimensional molecular data. However, a variety of factors related to experimental design may affect the ability to learn generalizable and clinically applicable diagnostics. Here, we argue that a causal perspective improves the identification of these challenges and formalizes their relation to the robustness and generalization of machine learning-based diagnostics. To make for a concrete discussion, we focus on a specific, recently established high-dimensional biomarker - adaptive immune receptor repertoires (AIRRs). Through simulations, we illustrate how major biological and experimental factors of the AIRR domain may influence the learned biomarkers. In conclusion, we argue that causal modeling improves machine learning-based biomarker robustness by identifying stable relations between variables and by guiding the adjustment of the relations and variables that vary between populations.

Well-established cognitive models coming from anthropology have shown that, due to the cognitive constraints that limit our "bandwidth" for social interactions, humans organize their social relations according to a regular structure. In this work, we postulate that similar regularities can be found in other cognitive processes, such as those involving language production. In order to investigate this claim, we analyse a dataset containing tweets of a heterogeneous group of Twitter users (regular users and professional writers). Leveraging a methodology similar to the one used to uncover the well-established social cognitive constraints, we find regularities at both the structural and semantic level. At the former, we find that a concentric layered structure (which we call ego network of words, in analogy to the ego network of social relationships) very well captures how individuals organise the words they use. The size of the layers in this structure regularly grows (approximately 2-3 times with respect to the previous one) when moving outwards, and the two penultimate external layers consistently account for approximately 60% and 30% of the used words, irrespective of the number of the total number of layers of the user. For the semantic analysis, each ring of each ego network is described by a semantic profile, which captures the topics associated with the words in the ring. We find that ring #1 has a special role in the model. It is semantically the most dissimilar and the most diverse among the rings. We also show that the topics that are important in the innermost ring also have the characteristic of being predominant in each of the other rings, as well as in the entire ego network. In this respect, ring #1 can be seen as the semantic fingerprint of the ego network of words.

Federated Learning (FL) is a distributed machine learning paradigm where clients collaboratively train a model using their local (human-generated) datasets. While existing studies focus on FL algorithm development to tackle data heterogeneity across clients, the important issue of data quality (e.g., label noise) in FL is overlooked. This paper aims to fill this gap by providing a quantitative study on the impact of label noise on FL. We derive an upper bound for the generalization error that is linear in the clients' label noise level. Then we conduct experiments on MNIST and CIFAR-10 datasets using various FL algorithms. Our empirical results show that the global model accuracy linearly decreases as the noise level increases, which is consistent with our theoretical analysis. We further find that label noise slows down the convergence of FL training, and the global model tends to overfit when the noise level is high.