We propose three new robust aggregation rules for distributed synchronous Stochastic Gradient Descent (SGD) under a general Byzantine failure model. The attackers can arbitrarily manipulate the data transferred between the servers and the workers in the parameter server (PS) architecture. We prove the Byzantine resilience properties of these aggregation rules. Empirical analysis shows that the proposed techniques outperform current approaches for realistic use cases and Byzantine attack scenarios.

How real is this relationship? This is a ubiquitous question that presents itself not only in judging interpersonal connections but also in evaluating correlations and causality throughout science and engineering. Two reasons for reaching incorrect conclusions based on observed relationships in collected data are chance and outside influences. For example, we can flip two coins that both show heads, or observe that today's temperature measurements on the west coast of the continental USA seem to correlate with tomorrow's on the east coast throughout the year. In the first case, we might not immediately conclude that coins are related, since the number of flips we observe is not very large relative to the possible variance of the process, and the apparent link we observed is up to chance. In the second case, we still may hesitate to use west coast weather to understand and predict east coast weather, since in reality both are closely following a seasonal trend. Establishing interpretable relationships between entities while mitigating the effects of chance can be achieved via sparse optimization methods, such as regression (Lasso) [1] and inverse covariance estimation [2]. In addition, the extension to time series via vector autoregression [3], [4] yields interpretations related to Granger causality [5]. In each of these settings, estimated nonzero values correspond to actual relations, while zeros correspond to absence of relations.

For a learning task, data can usually be collected from different sources or be represented from multiple views. For example, laboratory results from different medical examinations are available for disease diagnosis, and each of them can only reflect the health state of a person from a particular aspect/view. Therefore, different views provide complementary information for learning tasks. An effective integration of the multi-view information is expected to facilitate the learning performance. In this paper, we propose a general predictor, named multi-view machines (MVMs), that can effectively include all the possible interactions between features from multiple views. A joint factorization is embedded for the full-order interaction parameters which allows parameter estimation under sparsity. Moreover, MVMs can work in conjunction with different loss functions for a variety of machine learning tasks. A stochastic gradient descent method is presented to learn the MVM model. We further illustrate the advantages of MVMs through comparison with other methods for multi-view classification, including support vector machines (SVMs), support tensor machines (STMs) and factorization machines (FMs).

Factor analysis is broadly used as a powerful unsupervised machine learning tool for reconstruction of hidden features in recorded mixtures of signals. In the case of a linear approximation, the mixtures can be decomposed by a variety of model-free Blind Source Separation (BSS) algorithms. Most of the available BSS algorithms consider an instantaneous mixing of signals, while the case when the mixtures are linear combinations of signals with delays is less explored. Especially difficult is the case when the number of sources of the signals with delays is unknown and has to be determined from the data as well. To address this problem, in this paper, we present a new method based on Nonnegative Matrix Factorization (NMF) that is capable of identifying: (a) the unknown number of the sources, (b) the delays and speed of propagation of the signals, and (c) the locations of the sources. Our method can be used to decompose records of mixtures of signals with delays emitted by an unknown number of sources in a nondispersive medium, based only on recorded data. This is the case, for example, when electromagnetic signals from multiple antennas are received asynchronously; or mixtures of acoustic or seismic signals recorded by sensors located at different positions; or when a shift in frequency is induced by the Doppler effect. By applying our method to synthetic datasets, we demonstrate its ability to identify the unknown number of sources as well as the waveforms, the delays, and the strengths of the signals. Using Bayesian analysis, we also evaluate estimation uncertainties and identify the region of likelihood where the positions of the sources can be found.

This paper studies the problem of distributed stochastic optimization in an adversarial setting where, out of the $m$ machines which allegedly compute stochastic gradients every iteration, an $\alpha$-fraction are Byzantine, and can behave arbitrarily and adversarially. Our main result is a variant of stochastic gradient descent (SGD) which finds $\varepsilon$-approximate minimizers of convex functions in $T = \tilde{O}\big( \frac{1}{\varepsilon^2 m} + \frac{\alpha^2}{\varepsilon^2} \big)$ iterations. In contrast, traditional mini-batch SGD needs $T = O\big( \frac{1}{\varepsilon^2 m} \big)$ iterations, but cannot tolerate Byzantine failures. Further, we provide a lower bound showing that, up to logarithmic factors, our algorithm is information-theoretically optimal both in terms of sampling complexity and time complexity.

An important preprocessing step in most data analysis pipelines aims to extract a small set of sources that explain most of the data. Currently used algorithms for blind source separation (BSS), however, often fail to extract the desired sources and need extensive cross-validation. In contrast, their rarely used probabilistic counterparts can get away with little cross-validation and are more accurate and reliable but no simple and scalable implementations are available. Here we present a novel probabilistic BSS framework (DECOMPOSE) that can be flexibly adjusted to the data, is extensible and easy to use, adapts to individual sources and handles large-scale data through algorithmic efficiency. DECOMPOSE encompasses and generalises many traditional BSS algorithms such as PCA, ICA and NMF and we demonstrate substantial improvements in accuracy and robustness on artificial and real data.

Stochastic Gradient Descent (SGD) is a fundamental algorithm in machine learning, representing the optimization backbone for training several classic models, from regression to neural networks. Given the recent practical focus on distributed machine learning, significant work has been dedicated to the convergence properties of this algorithm under the inconsistent and noisy updates arising from execution in a distributed environment. However, surprisingly, the convergence properties of this classic algorithm in the standard shared-memory model are still not well-understood. In this work, we address this gap, and provide new convergence bounds for lock-free concurrent stochastic gradient descent, executing in the classic asynchronous shared memory model, against a strong adaptive adversary. Our results give improved upper and lower bounds on the "price of asynchrony" when executing the fundamental SGD algorithm in a concurrent setting. They show that this classic optimization tool can converge faster and with a wider range of parameters than previously known under asynchronous iterations. At the same time, we exhibit a fundamental trade-off between the maximum delay in the system and the rate at which SGD can converge, which governs the set of parameters under which this algorithm can still work efficiently.

When one is faced with a dataset too large to be used all at once, an obvious solution is to retain only part of it. In practice this takes a wide variety of different forms, but among them "coresets" are especially appealing. A coreset is a (small) weighted sample of the original data that comes with a guarantee: that a cost function can be evaluated on the smaller set instead of the larger one, with low relative error. For some classes of problems, and via a careful choice of sampling distribution, iid random sampling has turned to be one of the most successful methods to build coresets efficiently. However, independent samples are sometimes overly redundant, and one could hope that enforcing diversity would lead to better performance. The difficulty lies in proving coreset properties in non-iid samples. We show that the coreset property holds for samples formed with determinantal point processes (DPP). DPPs are interesting because they are a rare example of repulsive point processes with tractable theoretical properties, enabling us to construct general coreset theorems. We apply our results to the $k$-means problem, and give empirical evidence of the superior performance of DPP samples over state of the art methods.

We propose a Bayesian optimization algorithm for objective functions that are sums or integrals of expensive-to-evaluate functions, allowing noisy evaluations. These objective functions arise in multi-task Bayesian optimization for tuning machine learning hyperparameters, optimization via simulation, and sequential design of experiments with random environmental conditions. Our method is average-case optimal by construction when a single evaluation of the integrand remains within our evaluation budget. Achieving this one-step optimality requires solving a challenging value of information optimization problem, for which we provide a novel efficient discretization-free computational method. We also provide consistency proofs for our method in both continuum and discrete finite domains for objective functions that are sums. In numerical experiments comparing against previous state-of-the-art methods, including those that also leverage sum or integral structure, our method performs as well or better across a wide range of problems and offers significant improvements when evaluations are noisy or the integrand varies smoothly in the integrated variables.

Proteins are used in various applications by pharmaceutical, food, fuel, and many other industries and their usage is growing steadily (Kirk et al., 2002; Sanchez and Demain, 2010). Proteins have important advantages over chemical catalysts, as they are derived from renewable resources, are biodegradable and are often highly selective (Cherry and Fidantsef, 2003). Protein engineering is used to further improve the properties of proteins, for example to enhance their catalytic activity, modify their substrate specificity or to improve their thermostability (Rapley and Walker, 2000). Increasing the stability is an important aspect of protein engineering, as the proteins used in industry should be stable in the industrial process conditions, which often involve higher than ambient temperature and non-aqueous solvents (Bommarius et al., 2011). The properties of a protein are modified by introducing alterations to its amino acid sequence. Mutations in general tend to be destabilising, and if too many destabilising mutations are implemented, the protein may not remain functional without compensatory stabilising mutations (Tokuriki and Tawfik, 2009). The stability of a protein can be defined as the difference in Gibbs energy G between the folded and unfolded (or native and denaturated) state of the protein.