Private machine learning involves addition of noise while training, resulting in lower accuracy. Intuitively, greater stability can imply greater privacy and improve this privacy-utility tradeoff. We study this role of stability in private empirical risk minimization, where differential privacy is achieved by output perturbation, and establish a corresponding theoretical result showing that for strongly-convex loss functions, an algorithm with uniform stability of $\beta$ implies a bound of $O(\sqrt{\beta})$ on the scale of noise required for differential privacy. The result applies to both explicit regularization and to implicitly stabilized ERM, such as adaptations of Stochastic Gradient Descent that are known to be stable. Thus, it generalizes recent results that improve privacy through modifications to SGD, and establishes stability as the unifying perspective. It implies new privacy guarantees for optimizations with uniform stability guarantees, where a corresponding differential privacy guarantee was previously not known. Experimental results validate the utility of stability enhanced privacy in several problems, including application of elastic nets and feature selection.

In this paper, we propose a novel learning scheme called epoch-evolving Gaussian Process Guided Learning (GPGL), which aims at characterizing the correlation information between the batch-level distribution and the global data distribution. Such correlation information is encoded as context labels and needs renewal every epoch. With the guidance of the context label and ground truth label, GPGL scheme provides a more efficient optimization through updating the model parameters with a triangle consistency loss. Furthermore, our GPGL scheme can be further generalized and naturally applied to the current deep models, outperforming the existing batch-based state-of-the-art models on mainstream datasets (CIFAR-10, CIFAR-100, and Tiny-ImageNet) remarkably.

A great variety of natural and artificial systems can be represented as networks of elementary structural entities coupled by relations between them. The abstraction of such systems as networks helps us understand, predict and optimize their behaviour [1, 2]. In this sense, node and graph embeddings have been established as standard feature representations in many learning tasks for graphs and complex networks [3, 4]. Node embedding methods map each node of a graph into a low-dimensional vector, that can be then used to solve downstream tasks such as edge prediction, network reconstruction and node classification. Node embeddings have proven successful in achieving low-dimensional encoding of static network structures, but many real-world networks are inherently dynamic, with interactions among nodes changing over time [5]. Time-resolved networks are also the support of important dynamical processes, such as epidemic or rumor spreading, cascading failures, consensus formation, etc. [6] Time-resolved node embeddings have been shown to yield improved performance for predicting the outcome of dynamical processes over networks, such as information diffusion and disease spreading [7]. In this paper we propose a representation learning model that performs an implicit tensor factorization on different higher-order representations of time-varying graphs.

Quadratic discriminant analysis (QDA) is a widely used classification technique that generalizes the linear discriminant analysis (LDA) classifier to the case of distinct covariance matrices among classes. For the QDA classifier to yield high classification performance, an accurate estimation of the covariance matrices is required. Such a task becomes all the more challenging in high dimensional settings, wherein the number of observations is comparable with the feature dimension. A popular way to enhance the performance of QDA classifier under these circumstances is to regularize the covariance matrix, giving the name regularized QDA (R-QDA) to the corresponding classifier. In this work, we consider the case in which the population covariance matrix has a spiked covariance structure, a model that is often assumed in several applications. Building on the classical QDA, we propose a novel quadratic classification technique, the parameters of which are chosen such that the fisher-discriminant ratio is maximized. Numerical simulations show that the proposed classifier not only outperforms the classical R-QDA for both synthetic and real data but also requires lower computational complexity, making it suitable to high dimensional settings.

A new loss function is proposed for neural networks on classification tasks which extends the hinge loss by assigning gradients to its critical points. We will show that for a linear classifier on linearly separable data with fixed step size, the margin of this modified hinge loss converges to the $\ell_2$ max-margin at the rate of $\mathcal{O}( 1/t )$. This rate is fast when compared with the $\mathcal{O}(1/\log t)$ rate of exponential losses such as the logistic loss. Furthermore, empirical results suggest that this increased convergence speed carries over to ReLU networks.

Searching for accurate Machine and Deep Learning models is a computationally expensive and awfully energivorous process. A strategy which has been gaining recently importance to drastically reduce computational time and energy consumed is to exploit the availability of different information sources, with different computational costs and different "fidelity", typically smaller portions of a large dataset. The multi-source optimization strategy fits into the scheme of Gaussian Process based Bayesian Optimization. An Augmented Gaussian Process method exploiting multiple information sources (namely, AGP-MISO) is proposed. The Augmented Gaussian Process is trained using only "reliable" information among available sources. A novel acquisition function is defined according to the Augmented Gaussian Process. Computational results are reported related to the optimization of the hyperparameters of a Support Vector Machine (SVM) classifier using two sources: a large dataset - the most expensive one - and a smaller portion of it. A comparison with a traditional Bayesian Optimization approach to optimize the hyperparameters of the SVM classifier on the large dataset only is reported.

Current machine learning algorithms are designed to work with huge volumes of high dimensional data such as images. However, these algorithms are being increasingly deployed to resource constrained systems such as mobile devices and embedded systems. Even in cases where large computing infrastructure is available, the size of each data instance, as well as datasets, can provide a huge bottleneck in data transfer across communication channels. Also, there is a huge incentive both in energy and monetary terms in reducing both the computational and memory requirements of these algorithms. For non-parametric models that require to leverage the stored training data at the inference time, the increased cost in memory and computation could be even more problematic. In this work, we aim to reduce the volume of data these algorithms must process through an end-to-end two-stage neural subset selection model, where the first stage selects a set of candidate points using a conditionally independent Bernoulli mask followed by an iterative coreset selection via a conditional Categorical distribution. The subset selection model is trained by meta-learning with a distribution of sets. We validate our method on set reconstruction and classification tasks with feature selection as well as the selection of representative samples from a given dataset, on which our method outperforms relevant baselines. We also show in our experiments that our method enhances scalability of non-parametric models such as Neural Processes.

We provide the first global model recovery results for the IRLS (iteratively reweighted least squares) heuristic for robust regression problems. IRLS is known to offer excellent performance, despite bad initializations and data corruption, for several parameter estimation problems. Existing analyses of IRLS frequently require careful initialization, thus offering only local convergence guarantees. We remedy this by proposing augmentations to the basic IRLS routine that not only offer guaranteed global recovery, but in practice also outperform state-of-the-art algorithms for robust regression. Our routines are more immune to hyperparameter misspecification in basic regression tasks, as well as applied tasks such as linear-armed bandit problems. Our theoretical analyses rely on a novel extension of the notions of strong convexity and smoothness to weighted strong convexity and smoothness, and establishing that sub-Gaussian designs offer bounded weighted condition numbers. These notions may be useful in analyzing other algorithms as well.

In this paper, we cast fair machine learning as invariant machine learning. We first formulate a version of individual fairness that enforces invariance on certain sensitive sets. We then design a transport-based regularizer that enforces this version of individual fairness and develop an algorithm to minimize the regularizer efficiently. Our theoretical results guarantee the proposed approach trains certifiably fair ML models. Finally, in the experimental studies we demonstrate improved fairness metrics in comparison to several recent fair training procedures on three ML tasks that are susceptible to algorithmic bias.

Completely random measures provide a principled approach to creating flexible unsupervised models, where the number of latent features is infinite and the number of features that influence the data grows with the size of the data set. Due to the infinity the latent features, posterior inference requires either marginalization---resulting in dependence structures that prevent efficient computation via parallelization and conjugacy---or finite truncation, which arbitrarily limits the flexibility of the model. In this paper we present a novel Markov chain Monte Carlo algorithm for posterior inference that adaptively sets the truncation level using auxiliary slice variables, enabling efficient, parallelized computation without sacrificing flexibility. In contrast to past work that achieved this on a model-by-model basis, we provide a general recipe that is applicable to the broad class of completely random measure-based priors. The efficacy of the proposed algorithm is evaluated on several popular nonparametric models, demonstrating a higher effective sample size per second compared to algorithms using marginalization as well as a higher predictive performance compared to models employing fixed truncations.