The study of first-order optimization algorithms (FOA) typically starts with assumptions on the objective functions, most commonly smoothness and strong convexity. These metrics are used to tune the hyperparameters of FOA. We introduce a class of perturbations quantified via a new norm, called *-norm. We show that adding a small perturbation to the objective function has an equivalently small impact on the behavior of any FOA, which suggests that it should have a minor impact on the tuning of the algorithm. However, we show that smoothness and strong convexity can be heavily impacted by arbitrarily small perturbations, leading to excessively conservative tunings and convergence issues. In view of these observations, we propose a notion of continuity of the metrics, which is essential for a robust tuning strategy. Since smoothness and strong convexity are not continuous, we propose a comprehensive study of existing alternative metrics which we prove to be continuous. We describe their mutual relations and provide their guaranteed convergence rates for the Gradient Descent algorithm accordingly tuned. Finally we discuss how our work impacts the theoretical understanding of FOA and their performances.

Researchers have used social media data to estimate various macroeconomic indicators about public behaviors, mostly as a way to reduce surveying costs. One of the most widely cited economic indicator is consumer confidence index (CCI). Numerous studies in the past have focused on using social media, especially Twitter data, to predict CCI. However, the strong correlations disappeared when those models were tested with newer data according to a recent comprehensive survey. In this work, we revisit this problem of assessing the true potential of using social media data to measure CCI, by proposing a robust non-parametric Bayesian modeling framework grounded in Gaussian Process Regression (which provides both an estimate and an uncertainty associated with it). Integral to our framework is a principled experimentation methodology that demonstrates how digital data can be employed to reduce the frequency of surveys, and thus periodic polling would be needed only to calibrate our model. Via extensive experimentation we show how the choice of different micro-decisions, such as the smoothing interval, various types of lags etc. have an important bearing on the results. By using decadal data (2008-2019) from Reddit, we show that both monthly and daily estimates of CCI can, indeed, be reliably estimated at least several months in advance, and that our model estimates are far superior to those generated by the existing methods.

In this paper, we investigate the recommendation task in the most common scenario with implicit feedback (e.g., clicks, purchases). State-of-the-art methods in this direction usually cast the problem as to learn a personalized ranking on a set of items (e.g., webpages, products). The top-N results are then provided to users as recommendations, where the N is usually a fixed number pre-defined by the system according to some heuristic criteria (e.g., page size, screen size). There is one major assumption underlying this fixed-number recommendation scheme, i.e., there are always sufficient relevant items to users' preferences. Unfortunately, this assumption may not always hold in real-world scenarios. In some applications, there might be very limited candidate items to recommend, and some users may have very high relevance requirement in recommendation. In this way, even the top-1 ranked item may not be relevant to a user's preference. Therefore, we argue that it is critical to provide a dynamic-K recommendation, where the K should be different with respect to the candidate item set and the target user. We formulate this dynamic-K recommendation task as a joint learning problem with both ranking and classification objectives. The ranking objective is the same as existing methods, i.e., to create a ranking list of items according to users' interests. The classification objective is unique in this work, which aims to learn a personalized decision boundary to differentiate the relevant items from irrelevant items. Based on these ideas, we extend two state-of-the-art ranking-based recommendation methods, i.e., BPRMF and HRM, to the corresponding dynamic-K versions, namely DK-BPRMF and DK-HRM. Our experimental results on two datasets show that the dynamic-K models are more effective than the original fixed-N recommendation methods.

The ever-growing popularity and rapid improving of artificial intelligence (AI) have raised rethinking on the evolution of wireless networks. Mobile edge computing (MEC) provides a natural platform for AI applications since it is with rich computation resources to train machine learning (ML) models, as well as low-latency access to the data generated by mobile and internet of things (IoT) devices. In this paper, we present an infrastructure to perform ML tasks at an MEC server with the assistance of a reconfigurable intelligent surface (RIS). In contrast to conventional communication systems where the principal criterions are to maximize the throughput, we aim at maximizing the learning performance. Specifically, we minimize the maximum learning error of all participating users by jointly optimizing transmit power of mobile users, beamforming vectors of the base station (BS), and the phase-shift matrix of the RIS. An alternating optimization (AO)-based framework is proposed to optimize the three terms iteratively, where a successive convex approximation (SCA)-based algorithm is developed to solve the power allocation problem, closed-form expressions of the beamforming vectors are derived, and an alternating direction method of multipliers (ADMM)-based algorithm is designed together with an error level searching (ELS) framework to effectively solve the challenging nonconvex optimization problem of the phase-shift matrix. Simulation results demonstrate significant gains of deploying an RIS and validate the advantages of our proposed algorithms over various benchmarks. Lastly, a unified communication-training-inference platform is developed based on the CARLA platform and the SECOND network, and a use case (3D object detection in autonomous driving) for the proposed scheme is demonstrated on the developed platform.

As machine learning (ML) is being applied to a greater variety of practical problems, ensuring the reliability of ML is recognized as becoming increasingly important. Among several potential approaches to reliable ML, conditional selective inference (SI) is recognized as a promising approach for evaluating the statistical reliability of data-driven hypotheses selected by ML methods. The basic idea of conditional SI is to make inference on a data-driven hypothesis conditional on the selection event that the hypothesis is selected by analyzing the data with the ML algorithm. Conditional SI has been actively studied especially in the context of feature selection. Notably, Lee et al. [1] and Tibshirani et al. [2] proposed conditional SI methods for exact conditional inference on selected features by using Lasso and stepwise feature selection (SFS), respectively.

We consider privacy-preserving data analysis in the local model of differential privacy augmented with a shuffler. In this model, each user sends a locally differentially private report and these reports are then anonymized and randomly shuffled. Systems based on this model were first proposed in [BEMMRLRKTS17]. The authors of [EFMRTT19] showed that random shuffling of inputs to locally private protocols amplifies the privacy guarantee. Thus, when the collection of anonymized reports is viewed in the central model, the privacy guarantees are substantially stronger than the original local privacy guarantees. A similar result was shown for the binary randomized response by Cheu, Smith, Ullman, Zeber, and Zhilyaev [CSUZZ19] who also formalized a related shuffle model of privacy. The analysis in [EFMRTT19] relies on a more general result referred to as privacy amplification by shuffling. This result shows that privacy is amplified when the inputs are shuffled before applying local randomizers and holds even when local randomizers are chosen sequentially and adaptively. Allowing adaptive choice of local randomizers is necessary for analyzing iterative optimization algorithms such as stochastic gradient descent.

Monitoring network traffic data to detect any hidden patterns of anomalies is a challenging and time-consuming task that requires high computing resources. To this end, an appropriate summarization technique is of great importance, where it can be a substitute for the original data. However, the summarized data is under the threat of removing anomalies. Therefore, it is vital to create a summary that can reflect the same pattern as the original data. Therefore, in this paper, we propose an INtelligent Summarization approach for IDENTifying hidden anomalies, called INSIDENT. The proposed approach guarantees to keep the original data distribution in summarized data. Our approach is a clustering-based algorithm that dynamically maps original feature space to a new feature space by locally weighting features in each cluster. Therefore, in new feature space, similar samples are closer, and consequently, outliers are more detectable. Besides, selecting representatives based on cluster size keeps the same distribution as the original data in summarized data. INSIDENT can be used both as the preprocess approach before performing anomaly detection algorithms and anomaly detection algorithm. The experimental results on benchmark datasets prove a summary of the data can be a substitute for original data in the anomaly detection task.

We show that the influence of a subset of the training samples can be removed -- or "forgotten" -- from the weights of a network trained on large-scale image classification tasks, and we provide strong computable bounds on the amount of remaining information after forgetting. Inspired by real-world applications of forgetting techniques, we introduce a novel notion of forgetting in mixed-privacy setting, where we know that a "core" subset of the training samples does not need to be forgotten. While this variation of the problem is conceptually simple, we show that working in this setting significantly improves the accuracy and guarantees of forgetting methods applied to vision classification tasks. Moreover, our method allows efficient removal of all information contained in non-core data by simply setting to zero a subset of the weights with minimal loss in performance. We achieve these results by replacing a standard deep network with a suitable linear approximation. With opportune changes to the network architecture and training procedure, we show that such linear approximation achieves comparable performance to the original network and that the forgetting problem becomes quadratic and can be solved efficiently even for large models. Unlike previous forgetting methods on deep networks, ours can achieve close to the state-of-the-art accuracy on large scale vision tasks. In particular, we show that our method allows forgetting without having to trade off the model accuracy.

We describe the convex semi-infinite dual of the two-layer vector-output ReLU neural network training problem. This semi-infinite dual admits a finite dimensional representation, but its support is over a convex set which is difficult to characterize. In particular, we demonstrate that the non-convex neural network training problem is equivalent to a finite-dimensional convex copositive program. Our work is the first to identify this strong connection between the global optima of neural networks and those of copositive programs. We thus demonstrate how neural networks implicitly attempt to solve copositive programs via semi-nonnegative matrix factorization, and draw key insights from this formulation. We describe the first algorithms for provably finding the global minimum of the vector output neural network training problem, which are polynomial in the number of samples for a fixed data rank, yet exponential in the dimension. However, in the case of convolutional architectures, the computational complexity is exponential in only the filter size and polynomial in all other parameters. We describe the circumstances in which we can find the global optimum of this neural network training problem exactly with soft-thresholded SVD, and provide a copositive relaxation which is guaranteed to be exact for certain classes of problems, and which corresponds with the solution of Stochastic Gradient Descent in practice.

Leveraging algorithmic stability to derive sharp generalization bounds is a classic and powerful approach in learning theory. Since Vapnik and Chervonenkis [1974] first formalized the idea for analyzing SVMs, it has been utilized to study many fundamental learning algorithms (e.g., $k$-nearest neighbors [Rogers and Wagner, 1978], stochastic gradient method [Hardt et al., 2016], linear regression [Maurer, 2017], etc). In a recent line of great works by Feldman and Vondrak [2018, 2019] as well as Bousquet et al. [2020b], they prove a high probability generalization upper bound of order $\widetilde{\mathcal{O}}(\gamma +\frac{L}{\sqrt{n}})$ for any uniformly $\gamma$-stable algorithm and $L$-bounded loss function. Although much progress was achieved in proving generalization upper bounds for stable algorithms, our knowledge of lower bounds is rather limited. In fact, there is no nontrivial lower bound known ever since the study on uniform stability began [Bousquet and Elisseeff, 2002], to the best of our knowledge. In this paper we fill the gap by proving a tight generalization lower bound of order $\Omega(\gamma+\frac{L}{\sqrt{n}})$, which matches the best known upper bound up to logarithmic factors