As one of the most fundamental problems in machine learning, statistics and differential privacy, Differentially Private Stochastic Convex Optimization (DP-SCO) has been extensively studied in recent years. However, most of the previous work can only handle either regular data distribution or irregular data in the low dimensional space case. To better understand the challenges arising from irregular data distribution, in this paper we provide the first study on the problem of DP-SCO with heavy-tailed data in the high dimensional space. In the first part we focus on the problem over some polytope constraint (such as the $\ell_1$-norm ball). We show that if the loss function is smooth and its gradient has bounded second order moment, it is possible to get a (high probability) error bound (excess population risk) of $\tilde{O}(\frac{\log d}{(n\epsilon)^\frac{1}{3}})$ in the $\epsilon$-DP model, where $n$ is the sample size and $d$ is the dimensionality of the underlying space. Next, for LASSO, if the data distribution that has bounded fourth-order moments, we improve the bound to $\tilde{O}(\frac{\log d}{(n\epsilon)^\frac{2}{5}})$ in the $(\epsilon, \delta)$-DP model. In the second part of the paper, we study sparse learning with heavy-tailed data. We first revisit the sparse linear model and propose a truncated DP-IHT method whose output could achieve an error of $\tilde{O}(\frac{s^{*2}\log d}{n\epsilon})$, where $s^*$ is the sparsity of the underlying parameter. Then we study a more general problem over the sparsity ({\em i.e.,} $\ell_0$-norm) constraint, and show that it is possible to achieve an error of $\tilde{O}(\frac{s^{*\frac{3}{2}}\log d}{n\epsilon})$, which is also near optimal up to a factor of $\tilde{O}{(\sqrt{s^*})}$, if the loss function is smooth and strongly convex.

In this paper, we revisit the problem of Differentially Private Stochastic Convex Optimization (DP-SCO) and provide excess population risks for some special classes of functions that are faster than the previous results of general convex and strongly convex functions. In the first part of the paper, we study the case where the population risk function satisfies the Tysbakov Noise Condition (TNC) with some parameter $\theta>1$. Specifically, we first show that under some mild assumptions on the loss functions, there is an algorithm whose output could achieve an upper bound of $\tilde{O}((\frac{1}{\sqrt{n}}+\frac{\sqrt{d\log \frac{1}{\delta}}}{n\epsilon})^\frac{\theta}{\theta-1})$ for $(\epsilon, \delta)$-DP when $\theta\geq 2$, here $n$ is the sample size and $d$ is the dimension of the space. Then we address the inefficiency issue, improve the upper bounds by $\text{Poly}(\log n)$ factors and extend to the case where $\theta\geq \bar{\theta}>1$ for some known $\bar{\theta}$. Next we show that the excess population risk of population functions satisfying TNC with parameter $\theta>1$ is always lower bounded by $\Omega((\frac{d}{n\epsilon})^\frac{\theta}{\theta-1}) $ and $\Omega((\frac{\sqrt{d\log \frac{1}{\delta}}}{n\epsilon})^\frac{\theta}{\theta-1})$ for $\epsilon$-DP and $(\epsilon, \delta)$-DP, respectively. In the second part, we focus on a special case where the population risk function is strongly convex. Unlike the previous studies, here we assume the loss function is {\em non-negative} and {\em the optimal value of population risk is sufficiently small}. With these additional assumptions, we propose a new method whose output could achieve an upper bound of $O(\frac{d\log\frac{1}{\delta}}{n^2\epsilon^2}+\frac{1}{n^{\tau}})$ for any $\tau\geq 1$ in $(\epsilon,\delta)$-DP model if the sample size $n$ is sufficiently large.

Forecasting graph-based time-dependent data has many practical applications. This task is challenging as models need not only to capture spatial dependency and temporal dependency within the data, but also to leverage useful auxiliary information for accurate predictions. In this paper, we analyze limitations of state-of-the-art models on dealing with temporal dependency. To address this limitation, we propose GSA-Forecaster, a new deep learning model for forecasting graph-based time-dependent data. GSA-Forecaster leverages graph sequence attention (GSA), a new attention mechanism proposed in this paper, for effectively capturing temporal dependency. GSA-Forecaster embeds the graph structure of the data into its architecture to address spatial dependency. GSA-Forecaster also accounts for auxiliary information to further improve predictions. We evaluate GSA-Forecaster with large-scale real-world graph-based time-dependent data and demonstrate its effectiveness over state-of-the-art models with 6.7% RMSE and 5.8% MAPE reduction.

Rationality and emotion are two fundamental elements of humans. Endowing agents with rationality and emotion has been one of the major milestones in AI. However, in the field of conversational AI, most existing models only specialize in one aspect and neglect the other, which often leads to dull or unrelated responses. In this paper, we hypothesize that combining rationality and emotion into conversational agents can improve response quality. To test the hypothesis, we focus on one fundamental aspect of rationality, i.e., commonsense, and propose CARE, a novel model for commonsense-aware emotional response generation. Specifically, we first propose a framework to learn and construct commonsense-aware emotional latent concepts of the response given an input message and a desired emotion. We then propose three methods to collaboratively incorporate the latent concepts into response generation. Experimental results on two large-scale datasets support our hypothesis and show that our model can produce more accurate and commonsense-aware emotional responses and achieve better human ratings than state-of-the-art models that only specialize in one aspect.

In this paper, we consider the problem of designing Differentially Private (DP) algorithms for Stochastic Convex Optimization (SCO) on heavy-tailed data. The irregularity of such data violates some key assumptions used in almost all existing DP-SCO and DP-ERM methods, resulting in failure to provide the DP guarantees. To better understand this type of challenges, we provide in this paper a comprehensive study of DP-SCO under various settings. First, we consider the case where the loss function is strongly convex and smooth. For this case, we propose a method based on the sample-and-aggregate framework, which has an excess population risk of $\tilde{O}(\frac{d^3}{n\epsilon^4})$ (after omitting other factors), where $n$ is the sample size and $d$ is the dimensionality of the data. Then, we show that with some additional assumptions on the loss functions, it is possible to reduce the \textit{expected} excess population risk to $\tilde{O}(\frac{ d^2}{ n\epsilon^2 })$. To lift these additional conditions, we also provide a gradient smoothing and trimming based scheme to achieve excess population risks of $\tilde{O}(\frac{ d^2}{n\epsilon^2})$ and $\tilde{O}(\frac{d^\frac{2}{3}}{(n\epsilon^2)^\frac{1}{3}})$ for strongly convex and general convex loss functions, respectively, \textit{with high probability}. Experiments suggest that our algorithms can effectively deal with the challenges caused by data irregularity.

(Gradient) Expectation Maximization (EM) is a widely used algorithm for estimating the maximum likelihood of mixture models or incomplete data problems. A major challenge facing this popular technique is how to effectively preserve the privacy of sensitive data. Previous research on this problem has already lead to the discovery of some Differentially Private (DP) algorithms for (Gradient) EM. However, unlike in the non-private case, existing techniques are not yet able to provide finite sample statistical guarantees. To address this issue, we propose in this paper the first DP version of (Gradient) EM algorithm with statistical guarantees. Moreover, we apply our general framework to three canonical models: Gaussian Mixture Model (GMM), Mixture of Regressions Model (MRM) and Linear Regression with Missing Covariates (RMC). Specifically, for GMM in the DP model, our estimation error is near optimal in some cases. For the other two models, we provide the first finite sample statistical guarantees. Our theory is supported by thorough numerical experiments.

Although EM algorithm is well-known to converge to an empirically good local estimator (Wu et al., 1983), finite sample statistical guarantees for its performance have not been established until recent studies (Balakrishnan et al., 2017b)(Zhu et al., 2017),(Wang et al., 2015),(Yi and Caramanis, 2015). Specifically, the first local convergence theory and finite sample statistical rate of convergence for the classical EM and its gradient ascent variant (gradient EM) were established in (Balakrishnan et al., 2017b). Later, (Wang et al., 2015) extended the classical EM and gradient EM algorithms to the high dimensional sparse setting, and the key idea in their methods is an additional truncation step after the M-step, which can exploit the intrinsic sparse structure of the high dimensional latent variable models. Later on, (Yi and Caramanis, 2015) also studied the high dimensional sparse EM algorithm and proposed a method which uses a regularized M-estimator in the M-step. Recently, (Zhu et al., 2017) considered the computational issue of the previous methods of the problem in high dimensional sparse case.

Recently, many machine learning and statistical models such as non-linear regressions, the Single Index, Multi-index, Varying Coefficient Index Models and Two-layer Neural Networks can be reduced to or be seen as a special case of a new model which is called the \textit{Stochastic Linear Combination of Non-linear Regressions} model. However, due to the high non-convexity of the problem, there is no previous work study how to estimate the model. In this paper, we provide the first study on how to estimate the model efficiently and scalably. Specifically, we first show that with some mild assumptions, if the variate vector $x$ is multivariate Gaussian, then there is an algorithm whose output vectors have $\ell_2$-norm estimation errors of $O(\sqrt{\frac{p}{n}})$ with high probability, where $p$ is the dimension of $x$ and $n$ is the number of samples. The key idea of the proof is based on an observation motived by the Stein's lemma. Then we extend our result to the case where $x$ is bounded and sub-Gaussian using the zero-bias transformation, which could be seen as a generalization of the classic Stein's lemma. We also show that with some additional assumptions there is an algorithm whose output vectors have $\ell_\infty$-norm estimation errors of $O(\frac{1}{\sqrt{p}}+\sqrt{\frac{p}{n}})$ with high probability. We also provide a concrete example to show that there exists some link function which satisfies the previous assumptions. Finally, for both Gaussian and sub-Gaussian cases we propose a faster sub-sampling based algorithm and show that when the sub-sample sizes are large enough then the estimation errors will not be sacrificed by too much. Experiments for both cases support our theoretical results. To the best of our knowledge, this is the first work that studies and provides theoretical guarantees for the stochastic linear combination of non-linear regressions model.

We address the challenge of finding algorithms for online allocation (i.e. bipartite matching) using a machine learning approach. In this paper, we focus on the AdWords problem, which is a classical online budgeted matching problem of both theoretical and practical significance. In contrast to existing work, our goal is to accomplish algorithm design {\em tabula rasa}, i.e., without any human-provided insights or expert-tuned training data beyond specifying the objective and constraints of the optimization problem. We construct a framework based on insights and ideas from game theory, adversarial training and GANs Key to our approach is to generate adversarial examples that expose the weakness of any given algorithm. A unique challenge in our context is to generate complete examples from scratch rather than perturbing given examples and we demonstrate this can be accomplished for the Adwords problem. We use this framework to co-train an algorithm network and an adversarial network against each other until they converge to an equilibrium. This approach finds algorithms and adversarial examples that are consistent with known optimal results. Secondly, we address the question of robustness of the algorithm, namely can we design algorithms that are both strong under practical distributions, as well as exhibit robust performance against adversarial instances. To accomplish this, we train algorithm networks using a mixture of adversarial and practical distributions like power-laws; the resulting networks exhibit a smooth trade-off between the two input regimes.

Federated learning learns from scattered data by fusing collaborative models from local nodes. However, due to chaotic information distribution, the model fusion may suffer from structural misalignment with regard to unmatched parameters. In this work, we propose a novel federated learning framework to resolve this issue by establishing a firm structure-information alignment across collaborative models. Specifically, we design a feature-oriented regulation method ({$\Psi$-Net}) to ensure explicit feature information allocation in different neural network structures. Applying this regulating method to collaborative models, matchable structures with similar feature information can be initialized at the very early training stage. During the federated learning process under either IID or non-IID scenarios, dedicated collaboration schemes further guarantee ordered information distribution with definite structure matching, so as the comprehensive model alignment. Eventually, this framework effectively enhances the federated learning applicability to extensive heterogeneous settings, while providing excellent convergence speed, accuracy, and computation/communication efficiency.