We study the problem of minimizing a strongly convex, smooth function when we have noisy estimates of its gradient. We propose a novel multistage accelerated algorithm that is universally optimal in the sense that it achieves the optimal rate both in the deterministic and stochastic case and operates without knowledge of noise characteristics. The algorithm consists of stages that use a stochastic version of Nesterov's method with a specific restart and parameters selected to achieve the fastest reduction in the bias-variance terms in the convergence rate bounds. Papers published at the Neural Information Processing Systems Conference.

Using a low-dimensional parametrization of signals is a generic and powerful way to enhance performance in signal processing and statistical inference. A very popular and widely explored type of dimensionality reduction is sparsity; another type is generative modelling of signal distributions. Generative models based on neural networks, such as GANs or variational auto-encoders, are particularly performant and are gaining on applicability. In this paper we study spiked matrix models, where a low-rank matrix is observed through a noisy channel. This problem with sparse structure of the spikes has attracted broad attention in the past literature. Here, we replace the sparsity assumption by generative modelling, and investigate the consequences on statistical and algorithmic properties.

Belief propagation is a fundamental message-passing algorithm for probabilistic reasoning and inference in graphical models. While it is known to be exact on trees, in most applications belief propagation is run on graphs with cycles. Understanding the behavior of loopy'' belief propagation has been a major challenge for researchers in machine learning, and several positive convergence results for BP are known under strong assumptions which imply the underlying graphical model exhibits decay of correlations. We show that under a natural initialization, BP converges quickly to the global optimum of the Bethe free energy for Ising models on arbitrary graphs, as long as the Ising model is \emph{ferromagnetic} (i.e. This holds even though such models can exhibit long range correlations and may have multiple suboptimal BP fixed points.

Machine learning models have had discernible achievements in a myriad of applications. However, most of these models are black-boxes, and it is obscure how the decisions are made by them. This makes the models unreliable and untrustworthy. To provide insights into the decision making processes of these models, a variety of traditional interpretable models have been proposed. Moreover, to generate more human-friendly explanations, recent work on interpretability tries to answer questions related to causality such as "Why does this model makes such decisions?" or "Was it a specific feature that caused the decision made by the model?". In this work, models that aim to answer causal questions are referred to as causal interpretable models. The existing surveys have covered concepts and methodologies of traditional interpretability. In this work, we present a comprehensive survey on causal interpretable models from the aspects of the problems and methods. In addition, this survey provides in-depth insights into the existing evaluation metrics for measuring interpretability, which can help practitioners understand for what scenarios each evaluation metric is suitable.

We propose a disease classification model, called the QC-SPHARM, for the early detection of the Alzheimer's Disease (AD). The proposed QC-SPHARM can distinguish between normal control (NC) subjects and AD patients, as well as between amnestic mild cognitive impairment (aMCI) patients having high possibility progressing into AD and those who do not. Using the spherical harmonics (SPHARM) based registration, hippocampal surfaces segmented from the ADNI data are individually registered to a template surface constructed from the NC subjects using SPHARM. Local geometric distortions of the deformation from the template surface to each subject are quantified in terms of conformality distortions and curvatures distortions. The measurements are combined with the spherical harmonics coefficients and the total volume change of the subject from the template. Afterwards, a t-test based feature selection method incorporating the bagging strategy is applied to extract those local regions having high discriminating power of the two classes. The disease diagnosis machine can therefore be built using the data under the Support Vector Machine (SVM) setting. Using 110 NC subjects and 110 AD patients from the ADNI database, the proposed algorithm achieves 85:2% testing accuracy on 80 random samples as testing subjects, with the incorporation of surface geometry in the classification machine. Using 20 aMCI patients who has advanced to AD during a two-year period and another 20 aMCI patients who remain non-AD for the next two years, the algorithm achieves 81:2% accuracy using 10 randomly picked subjects as testing data. Our proposed method is 6%-15% better than other classification models without the incorporation of surface geometry. The results demonstrate the advantages of using local geometric distortions as the discriminating criterion for early AD diagnosis.

In this paper, the problem of minimizing energy and time consumption for task computation and transmission is studied in a mobile edge computing (MEC)-enabled balloon network. In the considered network, each user needs to process a computational task in each time instant, where high-altitude balloons (HABs), acting as flying wireless base stations, can use their powerful computational abilities to process the tasks offloaded from their associated users. Since the data size of each user's computational task varies over time, the HABs must dynamically adjust the user association, service sequence, and task partition scheme to meet the users' needs. This problem is posed as an optimization problem whose goal is to minimize the energy and time consumption for task computing and transmission by adjusting the user association, service sequence, and task allocation scheme. To solve this problem, a support vector machine (SVM)-based federated learning (FL) algorithm is proposed to determine the user association proactively. The proposed SVM-based FL method enables each HAB to cooperatively build an SVM model that can determine all user associations without any transmissions of either user historical associations or computational tasks to other HABs. Given the prediction of the optimal user association, the service sequence and task allocation of each user can be optimized so as to minimize the weighted sum of the energy and time consumption. Simulations with real data of city cellular traffic from the OMNILab at Shanghai Jiao Tong University show that the proposed algorithm can reduce the weighted sum of the energy and time consumption of all users by up to 16.1% compared to a conventional centralized method.

Recently, substantial research efforts in Deep Metric Learning (DML) focused on designing complex pairwise-distance losses and convoluted sample-mining and implementation strategies to ease optimization. The standard cross-entropy loss for classification has been largely overlooked in DML. On the surface, the cross-entropy may seem unrelated and irrelevant to metric learning as it does not explicitly involve pairwise distances. However, we provide a theoretical analysis that links the cross-entropy to several well-known and recent pairwise losses. Our connections are drawn from two different perspectives: one based on an explicit optimization insight; the other on discriminative and generative views of the mutual information between the labels and the learned features. First, we explicitly demonstrate that the cross-entropy is an upper bound on a new pairwise loss, which has a structure similar to various pairwise losses: it minimizes intra-class distances while maximizing inter-class distances. As a result, minimizing the cross-entropy can be seen as an approximate bound-optimization (or Majorize-Minimize) algorithm for minimizing this pairwise loss. Second, we show that, more generally, minimizing the cross-entropy is actually equivalent to maximizing the mutual information, to which we connect several well-known pairwise losses. These findings indicate that the cross-entropy represents a proxy for maximizing the mutual information -- as pairwise losses do -- without the need for complex sample-mining and optimization schemes. Furthermore, we show that various standard pairwise losses can be explicitly related to one another via bound relationships. Our experiments over four standard DML benchmarks (CUB200, Cars-196, Stanford Online Product and In-Shop) strongly support our findings. We consistently obtained state-of-the-art results, outperforming many recent and complex DML methods.

Recent studies have shown that deep neural networks (DNNs) are vulnerable to various attacks, including evasion attacks and poisoning attacks. On the defense side, there have been intensive interests in provable robustness against evasion attacks. In this paper, we focus on improving model robustness against more diverse threat models. Specifically, we provide the first unified framework using smoothing functional to certify the model robustness against general adversarial attacks. In particular, we propose the first robust training process RAB to certify against backdoor attacks. We theoretically prove the robustness bound for machine learning models based on the RAB training process, analyze the tightness of the robustness bound, as well as proposing different smoothing noise distributions such as Gaussian and Uniform distributions. Moreover, we evaluate the certified robustness of a family of "smoothed" DNNs which are trained in a differentially private fashion. In addition, we theoretically show that for simpler models such as K-nearest neighbor models, it is possible to train the robust smoothed models efficiently. For K=1, we propose an exact algorithm to smooth the training process, eliminating the need to sample from a noise distribution.Empirically, we conduct comprehensive experiments for different machine learning models such as DNNs, differentially private DNNs, and KNN models on MNIST, CIFAR-10 and ImageNet datasets to provide the first benchmark for certified robustness against backdoor attacks. In particular, we also evaluate KNN models on a spambase tabular dataset to demonstrate its advantages. Both the theoretic analysis for certified model robustness against arbitrary backdoors, and the comprehensive benchmark on diverse ML models and datasets would shed light on further robust learning strategies against training time or even general adversarial attacks on ML models.

We consider the variable selection problem of generalized linear models (GLMs). Stability selection (SS) is a promising method proposed for solving this problem. Although SS provides practical variable selection criteria, it is computationally demanding because it needs to fit GLMs to many re-sampled datasets. We propose a novel approximate inference algorithm that can conduct SS without the repeated fitting. The algorithm is based on the replica method of statistical mechanics and vector approximate message passing of information theory. For datasets characterized by rotation-invariant matrix ensembles, we derive state evolution equations that macroscopically describe the dynamics of the proposed algorithm. We also show that their fixed points are consistent with the replica symmetric solution obtained by the replica method. Numerical experiments indicate that the algorithm exhibits fast convergence and high approximation accuracy for both synthetic and real-world data.

A variety of real-world systems can be modeled as bipartite networks. One of the most powerful and simple link prediction methods is Linear-Graph Autoencoder(LGAE) which has promising performance on challenging tasks such as link prediction and node clustering. LGAE relies on simple linear model w.r.t. the adjacency matrix of the graph to learn vector space representations of nodes. In this paper, we consider the case of bipartite link predictions where node attributes are unavailable. When using LGAE, we propose to multiply the reconstructed adjacency matrix with a symmetrically normalized training adjacency matrix. As a result, 2-hop paths are formed which we use as the predicted adjacency matrix to evaluate the performance of our model. Experimental results on both synthetic and real-world dataset show our approach consistently outperforms Graph Autoencoder and Linear Graph Autoencoder model in 10 out of 12 bipartite dataset and reaches competitive performances in 2 other bipartite dataset.