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In this paper, we develop a novel high-dimensional coefficient estimation procedure based on high-frequency data. Unlike usual high-dimensional regression procedure such as LASSO, we additionally handle the heavy-tailedness of high-frequency observations as well as time variations of coefficient processes. Specifically, we employ Huber loss and truncation scheme to handle heavy-tailed observations, while $\ell_{1}$-regularization is adopted to overcome the curse of dimensionality under a sparse coefficient structure. To account for the time-varying coefficient, we estimate local high-dimensional coefficients which are biased estimators due to the $\ell_{1}$-regularization. Thus, when estimating integrated coefficients, we propose a debiasing scheme to enjoy the law of large number property and employ a thresholding scheme to further accommodate the sparsity of the coefficients. We call this Robust thrEsholding Debiased LASSO (RED-LASSO) estimator. We show that the RED-LASSO estimator can achieve a near-optimal convergence rate with only finite $\gamma$th moment for any $\gamma>2$. In the empirical study, we apply the RED-LASSO procedure to the high-dimensional integrated coefficient estimation using high-frequency trading data.

We introduce the Weak-form Estimation of Nonlinear Dynamics (WENDy) method for estimating model parameters for non-linear systems of ODEs. The core mathematical idea involves an efficient conversion of the strong form representation of a model to its weak form, and then solving a regression problem to perform parameter inference. The core statistical idea rests on the Errors-In-Variables framework, which necessitates the use of the iteratively reweighted least squares algorithm. Further improvements are obtained by using orthonormal test functions, created from a set of $C^{\infty}$ bump functions of varying support sizes. We demonstrate that WENDy is a highly robust and efficient method for parameter inference in differential equations. Without relying on any numerical differential equation solvers, WENDy computes accurate estimates and is robust to large (biologically relevant) levels of measurement noise. For low dimensional systems with modest amounts of data, WENDy is competitive with conventional forward solver-based nonlinear least squares methods in terms of speed and accuracy. For both higher dimensional systems and stiff systems, WENDy is typically both faster (often by orders of magnitude) and more accurate than forward solver-based approaches. We illustrate the method and its performance in some common population and neuroscience models, including logistic growth, Lotka-Volterra, FitzHugh-Nagumo, Hindmarsh-Rose, and a Protein Transduction Benchmark model. Software and code for reproducing the examples is available at (//github.com/MathBioCU/WENDy).

Federated optimization (FedOpt), which targets at collaboratively training a learning model across a large number of distributed clients, is vital for federated learning. The primary concerns in FedOpt can be attributed to the model divergence and communication efficiency, which significantly affect the performance. In this paper, we propose a new method, i.e., LoSAC, to learn from heterogeneous distributed data more efficiently. Its key algorithmic insight is to locally update the estimate for the global full gradient after {each} regular local model update. Thus, LoSAC can keep clients' information refreshed in a more compact way. In particular, we have studied the convergence result for LoSAC. Besides, the bonus of LoSAC is the ability to defend the information leakage from the recent technique Deep Leakage Gradients (DLG). Finally, experiments have verified the superiority of LoSAC comparing with state-of-the-art FedOpt algorithms. Specifically, LoSAC significantly improves communication efficiency by more than $100\%$ on average, mitigates the model divergence problem and equips with the defense ability against DLG.

In federated learning (FL), clients cooperatively train a global model without revealing their raw data but gradients or parameters, while the local information can still be disclosed from local outputs transmitted to the parameter server. With such privacy concerns, a client may overly add artificial noise to his local updates to compromise the global model training, and we prove the selfish noise adding leads to an infinite price of anarchy (PoA). This paper proposes a novel pricing mechanism to regulate privacy-sensitive clients without verifying their parameter updates, unlike existing privacy mechanisms that assume the server's full knowledge of added noise. Without knowing the ground truth, our mechanism reaches the social optimum to best balance the global training error and privacy loss, according to the difference between a client's updated parameter and all clients' average parameter. We also improve the FL convergence bound by refining the aggregation rule at the server to account for different clients' noise variances. Moreover, we extend our pricing scheme to fit incomplete information of clients' privacy sensitivities, ensuring their truthful type reporting and the system's ex-ante budget balance. Simulations show that our pricing scheme greatly improves the system performance especially when clients have diverse privacy sensitivities.

This paper proposes innovations to parameter estimation in a generalised logistic regression model in the context of detecting differential item functioning in multi-item measurements. The two newly proposed iterative algorithms are compared with existing methods in a simulation study, and their use is demonstrated in a real data example. Additionally the study examines software implementation including specification of initial values for iterative algorithms, and asymptotic properties with estimation of standard errors. Overall, the proposed methods gave comparable results to existing ones and were superior in some scenarios.

Machine learning models have been deployed in mobile networks to deal with massive data from different layers to enable automated network management and intelligence on devices. To overcome high communication cost and severe privacy concerns of centralized machine learning, federated learning (FL) has been proposed to achieve distributed machine learning among networked devices. While the computation and communication limitation has been widely studied, the impact of on-device storage on the performance of FL is still not explored. Without an effective data selection policy to filter the massive streaming data on devices, classical FL can suffer from much longer model training time ($4\times$) and significant inference accuracy reduction ($7\%$), observed in our experiments. In this work, we take the first step to consider the online data selection for FL with limited on-device storage. We first define a new data valuation metric for data evaluation and selection in FL with theoretical guarantees for speeding up model convergence and enhancing final model accuracy, simultaneously. We further design {\ttfamily ODE}, a framework of \textbf{O}nline \textbf{D}ata s\textbf{E}lection for FL, to coordinate networked devices to store valuable data samples. Experimental results on one industrial dataset and three public datasets show the remarkable advantages of {\ttfamily ODE} over the state-of-the-art approaches. Particularly, on the industrial dataset, {\ttfamily ODE} achieves as high as $2.5\times$ speedup of training time and $6\%$ increase in inference accuracy, and is robust to various factors in practical environments.

In recent years, Graph Neural Networks have reported outstanding performance in tasks like community detection, molecule classification and link prediction. However, the black-box nature of these models prevents their application in domains like health and finance, where understanding the models' decisions is essential. Counterfactual Explanations (CE) provide these understandings through examples. Moreover, the literature on CE is flourishing with novel explanation methods which are tailored to graph learning. In this survey, we analyse the existing Graph Counterfactual Explanation methods, by providing the reader with an organisation of the literature according to a uniform formal notation for definitions, datasets, and metrics, thus, simplifying potential comparisons w.r.t to the method advantages and disadvantages. We discussed seven methods and sixteen synthetic and real datasets providing details on the possible generation strategies. We highlight the most common evaluation strategies and formalise nine of the metrics used in the literature. We first introduce the evaluation framework GRETEL and how it is possible to extend and use it while providing a further dimension of comparison encompassing reproducibility aspects. Finally, we provide a discussion on how counterfactual explanation interplays with privacy and fairness, before delving into open challenges and future works.

As soon as abstract mathematical computations were adapted to computation on digital computers, the problem of efficient representation, manipulation, and communication of the numerical values in those computations arose. Strongly related to the problem of numerical representation is the problem of quantization: in what manner should a set of continuous real-valued numbers be distributed over a fixed discrete set of numbers to minimize the number of bits required and also to maximize the accuracy of the attendant computations? This perennial problem of quantization is particularly relevant whenever memory and/or computational resources are severely restricted, and it has come to the forefront in recent years due to the remarkable performance of Neural Network models in computer vision, natural language processing, and related areas. Moving from floating-point representations to low-precision fixed integer values represented in four bits or less holds the potential to reduce the memory footprint and latency by a factor of 16x; and, in fact, reductions of 4x to 8x are often realized in practice in these applications. Thus, it is not surprising that quantization has emerged recently as an important and very active sub-area of research in the efficient implementation of computations associated with Neural Networks. In this article, we survey approaches to the problem of quantizing the numerical values in deep Neural Network computations, covering the advantages/disadvantages of current methods. With this survey and its organization, we hope to have presented a useful snapshot of the current research in quantization for Neural Networks and to have given an intelligent organization to ease the evaluation of future research in this area.

This paper serves as a survey of recent advances in large margin training and its theoretical foundations, mostly for (nonlinear) deep neural networks (DNNs) that are probably the most prominent machine learning models for large-scale data in the community over the past decade. We generalize the formulation of classification margins from classical research to latest DNNs, summarize theoretical connections between the margin, network generalization, and robustness, and introduce recent efforts in enlarging the margins for DNNs comprehensively. Since the viewpoint of different methods is discrepant, we categorize them into groups for ease of comparison and discussion in the paper. Hopefully, our discussions and overview inspire new research work in the community that aim to improve the performance of DNNs, and we also point to directions where the large margin principle can be verified to provide theoretical evidence why certain regularizations for DNNs function well in practice. We managed to shorten the paper such that the crucial spirit of large margin learning and related methods are better emphasized.

For deploying a deep learning model into production, it needs to be both accurate and compact to meet the latency and memory constraints. This usually results in a network that is deep (to ensure performance) and yet thin (to improve computational efficiency). In this paper, we propose an efficient method to train a deep thin network with a theoretic guarantee. Our method is motivated by model compression. It consists of three stages. In the first stage, we sufficiently widen the deep thin network and train it until convergence. In the second stage, we use this well-trained deep wide network to warm up (or initialize) the original deep thin network. This is achieved by letting the thin network imitate the immediate outputs of the wide network from layer to layer. In the last stage, we further fine tune this well initialized deep thin network. The theoretical guarantee is established by using mean field analysis, which shows the advantage of layerwise imitation over traditional training deep thin networks from scratch by backpropagation. We also conduct large-scale empirical experiments to validate our approach. By training with our method, ResNet50 can outperform ResNet101, and BERT_BASE can be comparable with BERT_LARGE, where both the latter models are trained via the standard training procedures as in the literature.