Deep neural networks, when optimized with sufficient data, provide accurate representations of high-dimensional functions; in contrast, function approximation techniques that have predominated in scientific computing do not scale well with dimensionality. As a result, many high-dimensional sampling and approximation problems once thought intractable are being revisited through the lens of machine learning. While the promise of unparalleled accuracy may suggest a renaissance for applications that require parameterizing representations of complex systems, in many applications gathering sufficient data to develop such a representation remains a significant challenge. Here we introduce an approach that combines rare events sampling techniques with neural network optimization to optimize objective functions that are dominated by rare events. We show that importance sampling reduces the asymptotic variance of the solution to a learning problem, suggesting benefits for generalization. We study our algorithm in the context of learning dynamical transition pathways between two states of a system, a problem with applications in statistical physics and implications in machine learning theory. Our numerical experiments demonstrate that we can successfully learn even with the compounding difficulties of high-dimension and rare data.

The adoption of "human-in-the-loop" paradigms in computer vision and machine learning is leading to various applications where the actual data acquisition (e.g., human supervision) and the underlying inference algorithms are closely interwined. While classical work in active learning provides effective solutions when the learning module involves classification and regression tasks, many practical issues such as partially observed measurements, financial constraints and even additional distributional or structural aspects of the data typically fall outside the scope of this treatment. For instance, with sequential acquisition of partial measurements of data that manifest as a matrix (or tensor), novel strategies for completion (or collaborative filtering) of the remaining entries have only been studied recently. Motivated by vision problems where we seek to annotate a large dataset of images via a crowdsourced platform or alternatively, complement results from a state-of-the-art object detector using human feedback, we study the "completion" problem defined on graphs, where requests for additional measurements must be made sequentially. We design the optimization model in the Fourier domain of the graph describing how ideas based on adaptive submodularity provide algorithms that work well in practice. On a large set of images collected from Imgur, we see promising results on images that are otherwise difficult to categorize. We also show applications to an experimental design problem in neuroimaging.

This paper is concerned with a state-space approach to deep Gaussian process (DGP) regression. We construct the DGP by hierarchically putting transformed Gaussian process (GP) priors on the length scales and magnitudes of the next level of Gaussian processes in the hierarchy. The idea of the state-space approach is to represent the DGP as a non-linear hierarchical system of linear stochastic differential equations (SDEs), where each SDE corresponds to a conditional GP. The DGP regression problem then becomes a state estimation problem, and we can estimate the state efficiently with sequential methods by using the Markov property of the state-space DGP. The computational complexity scales linearly with respect to the number of measurements. Based on this, we formulate state-space MAP as well as Bayesian filtering and smoothing solutions to the DGP regression problem. We demonstrate the performance of the proposed models and methods on synthetic non-stationary signals and apply the state-space DGP to detection of the gravitational waves from LIGO measurements.

This report considers the problem of Byzantine fault-tolerance in homogeneous multi-agent distributed learning. In this problem, each agent samples i.i.d. data points, and the goal for the agents is to compute a mathematical model that optimally fits, in expectation, the data points sampled by all the agents. We consider the case when a certain number of agents may be Byzantine faulty. Such faulty agents may not follow a prescribed learning algorithm. Faulty agents may share arbitrary incorrect information regarding their data points to prevent the non-faulty agents from learning a correct model. We propose a fault-tolerance mechanism for the distributed stochastic gradient descent (D-SGD) method -- a standard distributed supervised learning algorithm. Our fault-tolerance mechanism relies on a norm based gradient-filter, named comparative gradient elimination (CGE), that aims to mitigate the detrimental impact of malicious incorrect stochastic gradients shared by the faulty agents by limiting their Euclidean norms. We show that the CGE gradient-filter guarantees fault-tolerance against a bounded number of Byzantine faulty agents if the stochastic gradients computed by the non-faulty agents satisfy the standard assumption of bounded variance. We demonstrate the applicability of the CGE gradient-filer for distributed supervised learning of artificial neural networks. We show that the fault-tolerance by the CGE gradient-filter is comparable to that by other state-of-the-art gradient-filters, namely the multi-KRUM, geometric median of means, and coordinate-wise trimmed mean. Lastly, we propose a gradient averaging scheme that aims to reduce the sensitivity of a supervised learning process to individual agents' data batch-sizes. We show that gradient averaging improves the fault-tolerance property of a gradient-filter, including, but not limited to, the CGE gradient-filter.

Open set classification (OSC) tackles the problem of determining whether the data are in-class or out-of-class during inference, when only provided with a set of in-class examples at training time. Traditional OSC methods usually train discriminative or generative models with in-class data, then utilize the pre-trained models to classify test data directly. However, these methods always suffer from embedding confusion problem, i.e., partial out-of-class instances are mixed with in-class ones of similar semantics, making it difficult to classify. To solve this problem, we unify semi-supervised learning to develop a novel OSC algorithm, S2OSC, that incorporates out-of-class instances filtering and model re-training in a transductive manner. In detail, given a pool of newly coming test data, S2OSC firstly filters distinct out-of-class instances using the pre-trained model, and annotates super-class for them. Then, S2OSC trains a holistic classification model by combing in-class and out-of-class labeled data and remaining unlabeled test data in semi-supervised paradigm, which also integrates pre-trained model for knowledge distillation to further separate mixed instances. Despite its simplicity, the experimental results show that S2OSC achieves state-of-the-art performance across a variety of OSC tasks, including 85.4% of F1 on CIFAR-10 with only 300 pseudo-labels. We also demonstrate how S2OSC can be expanded to incremental OSC setting effectively with streaming data.

We propose a stochastic recursive momentum method for Riemannian non-convex optimization that achieves a near-optimal complexity of $\tilde{\mathcal{O}}(\epsilon^{-3})$ to find $\epsilon$-approximate solution with one sample. That is, our method requires $\mathcal{O}(1)$ gradient evaluations per iteration and does not require restarting with a large batch gradient, which is commonly used to obtain the faster rate. Extensive experiment results demonstrate the superiority of our proposed algorithm.

We study the problem of recovering an unknown signal $\boldsymbol x$ given measurements obtained from a generalized linear model with a Gaussian sensing matrix. Two popular solutions are based on a linear estimator $\hat{\boldsymbol x}^{\rm L}$ and a spectral estimator $\hat{\boldsymbol x}^{\rm s}$. The former is a data-dependent linear combination of the columns of the measurement matrix, and its analysis is quite simple. The latter is the principal eigenvector of a data-dependent matrix, and a recent line of work has studied its performance. In this paper, we show how to optimally combine $\hat{\boldsymbol x}^{\rm L}$ and $\hat{\boldsymbol x}^{\rm s}$. At the heart of our analysis is the exact characterization of the joint empirical distribution of $(\boldsymbol x, \hat{\boldsymbol x}^{\rm L}, \hat{\boldsymbol x}^{\rm s})$ in the high-dimensional limit. This allows us to compute the Bayes-optimal combination of $\hat{\boldsymbol x}^{\rm L}$ and $\hat{\boldsymbol x}^{\rm s}$, given the limiting distribution of the signal $\boldsymbol x$. When the distribution of the signal is Gaussian, then the Bayes-optimal combination has the form $\theta\hat{\boldsymbol x}^{\rm L}+\hat{\boldsymbol x}^{\rm s}$ and we derive the optimal combination coefficient. In order to establish the limiting distribution of $(\boldsymbol x, \hat{\boldsymbol x}^{\rm L}, \hat{\boldsymbol x}^{\rm s})$, we design and analyze an Approximate Message Passing (AMP) algorithm whose iterates give $\hat{\boldsymbol x}^{\rm L}$ and approach $\hat{\boldsymbol x}^{\rm s}$. Numerical simulations demonstrate the improvement of the proposed combination with respect to the two methods considered separately.

Federated learning (FL) is an emerging paradigm for distributed training of large-scale deep neural networks in which participants' data remains on their own devices with only model updates being shared with a central server. However, the distributed nature of FL gives rise to new threats caused by potentially malicious participants. In this paper, we study targeted data poisoning attacks against FL systems in which a malicious subset of the participants aim to poison the global model by sending model updates derived from mislabeled data. We first demonstrate that such data poisoning attacks can cause substantial drops in classification accuracy and recall, even with a small percentage of malicious participants. We additionally show that the attacks can be targeted, i.e., they have a large negative impact only on classes that are under attack. We also study attack longevity in early/late round training, the impact of malicious participant availability, and the relationships between the two. Finally, we propose a defense strategy that can help identify malicious participants in FL to circumvent poisoning attacks, and demonstrate its effectiveness.

While these statements are humorous, it's not at all obvious what data science encompasses. There have been many data science Venn diagrams and many definitions over the years. However, in my research, the ones I found were either convoluted or missing one of the three core data science functions. In this article, you'll learn about the three primary parts of data science. You'll also learn about an emerging type of data science project. Finally, you'll see two other areas that are important to data science, but not quite part of the core.

"We applied machine learning algorithms (artificial neural networks, support vector machines, and random forest models) that predicted separation …