Machine learning algorithms have exciting and wide-range potential. However, as the data frequently containsensitive personal information, there are real privacy concerns associated with the development and the deployment of this technology. Motivated by this observation, the line of work on differentially private learning (initiated by [23]) aims to construct learning algorithms that provide strong (mathematically proven) privacy protections for the training data. Both government agenciesand industrial companies have realized the importance of introducing strong privacy protection to statistical and machine learning tasks. A few recent examples include Google [20] and Apple [27] that are already using differentially private estimation algorithms that feed into machine learning algorithms, and the US Census Bureau announcement that they will use differentially privatedata publication techniques in the next decennial census [1]. Differential privacy is increasingly accepted as a standard for rigorous privacy. We refer the reader to the excellent surveys in [17] and [28]. The definition of differential privacy is, Definition 1.1 ([16]). Let A be a randomized algorithm whose input is a sample.

To relieve the pain of manually selecting machine learning algorithms and tuning hyperparameters, automated machine learning (AutoML) methods have been developed to automatically search for good models. Due to the huge model search space, it is impossible to try all models. Users tend to distrust automatic results and increase the search budget as much as they can, thereby undermining the efficiency of AutoML. To address these issues, we design and implement ATMSeer, an interactive visualization tool that supports users in refining the search space of AutoML and analyzing the results. To guide the design of ATMSeer, we derive a workflow of using AutoML based on interviews with machine learning experts. A multi-granularity visualization is proposed to enable users to monitor the AutoML process, analyze the searched models, and refine the search space in real time. We demonstrate the utility and usability of ATMSeer through two case studies, expert interviews, and a user study with 13 end users.

A promising direction in deep learning research consists in learning representations and simultaneously discovering cluster structure in unlabeled data by optimizing a discriminative loss function. As opposed to supervised deep learning, this line of research is in its infancy, and how to design and optimize suitable loss functions to train deep neural networks for clustering is still an open question. Our contribution to this emerging field is a new deep clustering network that leverages the discriminative power of information-theoretic divergence measures, which have been shown to be effective in traditional clustering. We propose a novel loss function that incorporates geometric regularization constraints, thus avoiding degenerate structures of the resulting clustering partition. Experiments on synthetic benchmarks and real datasets show that the proposed network achieves competitive performance with respect to other state-of-the-art methods, scales well to large datasets, and does not require pre-training steps.

Subsampled Newton methods approximate Hessian matrices through subsampling techniques, alleviating the cost of forming Hessian matrices but using sufficient curvature information. However, previous results require $\Omega (d)$ samples to approximate Hessians, where $d$ is the dimension of data points, making it less practically feasible for high-dimensional data. The situation is deteriorated when $d$ is comparably as large as the number of data points $n$, which requires to take the whole dataset into account, making subsampling useless. This paper theoretically justifies the effectiveness of subsampled Newton methods on high dimensional data. Specifically, we prove only $\widetilde{\Theta}(d^\gamma_{\rm eff})$ samples are needed in the approximation of Hessian matrices, where $d^\gamma_{\rm eff}$ is the $\gamma$-ridge leverage and can be much smaller than $d$ as long as $n\gamma \gg 1$. Additionally, we extend this result so that subsampled Newton methods can work for high-dimensional data on both distributed optimization problems and non-smooth regularized problems.

We present a novel and hierarchical approach for supervised classification of signals spanning over a fixed graph, reflecting shared properties of the dataset. To this end, we introduce a Convolutional Cluster Pooling layer exploiting a multi-scale clustering in order to highlight, at different resolutions, locally connected regions on the input graph. Our proposal generalises well-established neural models such as Convolutional Neural Networks (CNNs) on irregular and complex domains, by means of the exploitation of the weight sharing property in a graph-oriented architecture. In this work, such property is based on the centrality of each vertex within its soft-assigned cluster. Extensive experiments on NTU RGB+D, CIFAR-10 and 20NEWS demonstrate the effectiveness of the proposed technique in capturing both local and global patterns in graph-structured data out of different domains.

This paper considers the perturbed stochastic gradient descent algorithm and shows that it finds $\epsilon$-second order stationary points ($\left\|\nabla f(x)\right\|\leq \epsilon$ and $\nabla^2 f(x) \succeq -\sqrt{\epsilon} \mathbf{I}$) in $\tilde{O}(d/\epsilon^4)$ iterations, giving the first result that has linear dependence on dimension for this setting. For the special case, where stochastic gradients are Lipschitz, the dependence on dimension reduces to polylogarithmic. In addition to giving new results, this paper also presents a simplified proof strategy that gives a shorter and more elegant proof of previously known results (Jin et al. 2017) on perturbed gradient descent algorithm.

We study the expressive power of kernel methods and the algorithmic feasibility of multiple kernel learning for a special rich class of kernels. Specifically, we define \emph{Euclidean kernels}, a diverse class that includes most, if not all, families of kernels studied in literature such as polynomial kernels and radial basis functions. We then describe the geometric and spectral structure of this family of kernels over the hypercube (and to some extent for any compact domain). Our structural results allow us to prove meaningful limitations on the expressive power of the class as well as derive several efficient algorithms for learning kernels over different domains.

Consider a Markov decision process (MDP) that admits a set of state-action features, which can linearly express the process's probabilistic transition model. We propose a parametric Q-learning algorithm that finds an approximate-optimal policy using a sample size proportional to the feature dimension $K$ and invariant with respect to the size of the state space. To further improve its sample efficiency, we exploit the monotonicity property and intrinsic noise structure of the Bellman operator, provided the existence of anchor state-actions that imply implicit non-negativity in the feature space. We augment the algorithm using techniques of variance reduction, monotonicity preservation, and confidence bounds. It is proved to find a policy which is $\epsilon$-optimal from any initial state with high probability using $\widetilde{O}(K/\epsilon^2(1-\gamma)^3)$ sample transitions for arbitrarily large-scale MDP with a discount factor $\gamma\in(0,1)$. A matching information-theoretical lower bound is proved, confirming the sample optimality of the proposed method with respect to all parameters (up to polylog factors).

We study online linear regression problems in a distributed setting, where the data is spread over a network. In each round, each network node proposes a linear predictor, with the objective of fitting the \emph{network-wide} data. It then updates its predictor for the next round according to the received local feedback and information received from neighboring nodes. The predictions made at a given node are assessed through the notion of regret, defined as the difference between their cumulative network-wide square errors and those of the best off-line network-wide linear predictor. Various scenarios are investigated, depending on the nature of the local feedback (full information or bandit feedback), on the set of available predictors (the decision set), and the way data is generated (by an oblivious or adaptive adversary). We propose simple and natural distributed regression algorithms, involving, at each node and in each round, a local gradient descent step and a communication and averaging step where nodes aim at aligning their predictors to those of their neighbors. We establish regret upper bounds typically in ${\cal O}(T^{3/4})$ when the decision set is unbounded and in ${\cal O}(\sqrt{T})$ in case of bounded decision set.

Manifold regularization, such as laplacian regularized least squares (LapRLS) and laplacian support vector machine (LapSVM), has been widely used in semi-supervised learning, and its performance greatly depends on the choice of some hyper-parameters. Cross-validation (CV) is the most popular approach for selecting the optimal hyper-parameters, but it has high complexity due to multiple times of learner training. In this paper, we provide a method to approximate the CV for manifold regularization based on a notion of robust statistics, called Bouligand influence function (BIF). We first provide a strategy for approximating the CV via the Taylor expansion of BIF. Then, we show how to calculate the BIF for general loss function,and further give the approximate CV criteria for model selection in manifold regularization. The proposed approximate CV for manifold regularization requires training only once, hence can significantly improve the efficiency of traditional CV. Experimental results show that our approximate CV has no statistical discrepancy with the original one, but much smaller time cost.