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Federated learning (FL) enables distributed devices to jointly train a shared model while keeping the training data local. Different from the horizontal FL (HFL) setting where each client has partial data samples, vertical FL (VFL), which allows each client to collect partial features, has attracted intensive research efforts recently. In this paper, we identified two challenges that state-of-the-art VFL frameworks are facing: (1) some works directly average the learned feature embeddings and therefore might lose the unique properties of each local feature set; (2) server needs to communicate gradients with the clients for each training step, incurring high communication cost that leads to rapid consumption of privacy budgets. In this paper, we aim to address the above challenges and propose an efficient VFL with multiple linear heads (VIM) framework, where each head corresponds to local clients by taking the separate contribution of each client into account. In addition, we propose an Alternating Direction Method of Multipliers (ADMM)-based method to solve our optimization problem, which reduces the communication cost by allowing multiple local updates in each step, and thus leads to better performance under differential privacy. We consider various settings including VFL with model splitting and without model splitting. For both settings, we carefully analyze the differential privacy mechanism for our framework. Moreover, we show that a byproduct of our framework is that the weights of learned linear heads reflect the importance of local clients. We conduct extensive evaluations and show that on four real-world datasets, VIM achieves significantly higher performance and faster convergence compared with state-of-the-arts. We also explicitly evaluate the importance of local clients and show that VIM enables functionalities such as client-level explanation and client denoising.

Boosting is one of the most significant developments in machine learning. This paper studies the rate of convergence of $L_2$Boosting, which is tailored for regression, in a high-dimensional setting. Moreover, we introduce so-called \textquotedblleft post-Boosting\textquotedblright. This is a post-selection estimator which applies ordinary least squares to the variables selected in the first stage by $L_2$Boosting. Another variant is \textquotedblleft Orthogonal Boosting\textquotedblright\ where after each step an orthogonal projection is conducted. We show that both post-$L_2$Boosting and the orthogonal boosting achieve the same rate of convergence as LASSO in a sparse, high-dimensional setting. We show that the rate of convergence of the classical $L_2$Boosting depends on the design matrix described by a sparse eigenvalue constant. To show the latter results, we derive new approximation results for the pure greedy algorithm, based on analyzing the revisiting behavior of $L_2$Boosting. We also introduce feasible rules for early stopping, which can be easily implemented and used in applied work. Our results also allow a direct comparison between LASSO and boosting which has been missing from the literature. Finally, we present simulation studies and applications to illustrate the relevance of our theoretical results and to provide insights into the practical aspects of boosting. In these simulation studies, post-$L_2$Boosting clearly outperforms LASSO.

We establish the minimax risk for parameter estimation in sparse high-dimensional Gaussian mixture models and show that a constrained maximum likelihood estimator (MLE) achieves the minimax optimality. However, the optimization-based constrained MLE is computationally intractable due to non-convexity of the problem. Therefore, we propose a Bayesian approach to estimate high-dimensional Gaussian mixtures whose cluster centers exhibit sparsity using a continuous spike-and-slab prior, and prove that the posterior contraction rate of the proposed Bayesian method is minimax optimal. The mis-clustering rate is obtained as a by-product using tools from matrix perturbation theory. Computationally, posterior inference of the proposed Bayesian method can be implemented via an efficient Gibbs sampler with data augmentation, circumventing the challenging frequentist nonconvex optimization-based algorithms. The proposed Bayesian sparse Gaussian mixture model does not require pre-specifying the number of clusters, which is allowed to grow with the sample size and can be adaptively estimated via posterior inference. The validity and usefulness of the proposed method is demonstrated through simulation studies and the analysis of a real-world single-cell RNA sequencing dataset.

Heterogeneity is a dominant factor in the behaviour of many biological processes. Despite this, it is common for mathematical and statistical analyses to ignore biological heterogeneity as a source of variability in experimental data. Therefore, methods for exploring the identifiability of models that explicitly incorporate heterogeneity through variability in model parameters are relatively underdeveloped. We develop a new likelihood-based framework, based on moment matching, for inference and identifiability analysis of differential equation models that capture biological heterogeneity through parameters that vary according to probability distributions. As our novel method is based on an approximate likelihood function, it is highly flexible; we demonstrate identifiability analysis using both a frequentist approach based on profile likelihood, and a Bayesian approach based on Markov-chain Monte Carlo. Through three case studies, we demonstrate our method by providing a didactic guide to inference and identifiability analysis of hyperparameters that relate to the statistical moments of model parameters from independent observed data. Our approach has a computational cost comparable to analysis of models that neglect heterogeneity, a significant improvement over many existing alternatives. We demonstrate how analysis of random parameter models can aid better understanding of the sources of heterogeneity from biological data.

This paper studies the design of two-wave experiments in the presence of spillover effects when the researcher aims to conduct precise inference on treatment effects. We consider units connected through a single network, local dependence among individuals, and a general class of estimands encompassing average treatment and average spillover effects. We introduce a statistical framework for designing two-wave experiments with networks, where the researcher optimizes over participants and treatment assignments to minimize the variance of the estimators of interest, using a first-wave (pilot) experiment to estimate the variance. We derive guarantees for inference on treatment effects and regret guarantees on the variance obtained from the proposed design mechanism. Our results illustrate the existence of a trade-off in the choice of the pilot study and formally characterize the pilot's size relative to the main experiment. Simulations using simulated and real-world networks illustrate the advantages of the method.

Object reconstruction from 3D point clouds has achieved impressive progress in the computer vision and computer graphics research field. However, reconstruction from time-varying point clouds (a.k.a. 4D point clouds) is generally overlooked. In this paper, we propose a new network architecture, namely RFNet-4D, that jointly reconstruct objects and their motion flows from 4D point clouds. The key insight is that simultaneously performing both tasks via learning spatial and temporal features from a sequence of point clouds can leverage individual tasks, leading to improved overall performance. To prove this ability, we design a temporal vector field learning module using unsupervised learning approach for flow estimation, leveraged by supervised learning of spatial structures for object reconstruction. Extensive experiments and analyses on benchmark dataset validated the effectiveness and efficiency of our method. As shown in experimental results, our method achieves state-of-the-art performance on both flow estimation and object reconstruction while performing much faster than existing methods in both training and inference. Our code and data are available at //github.com/hkust-vgd/RFNet-4D

We showcase a variety of functions and classes that implement sampling procedures with improved exploration of the parameter space assisted by machine learning. Special attention is paid to setting sane defaults with the objective that adjustments required by different problems remain minimal. This collection of routines can be employed for different types of analysis, from finding bounds on the parameter space to accumulating samples in areas of interest. In particular, we discuss two methods assisted by incorporating different machine learning models: regression and classification. We show that a machine learning classifier can provide higher efficiency for exploring the parameter space. Also, we introduce a boosting technique to improve the slow convergence at the start of the process. The use of these routines is better explained with the help of a few examples that illustrate the type of results one can obtain. We also include examples of the code used to obtain the examples as well as descriptions of the adjustments that can be made to adapt the calculation to other problems. We finalize by showing the impact of these techniques when exploring the parameter space of the two Higgs doublet model that matches the measured Higgs Boson signal strength. The code used for this paper and instructions on how to use it are available on the web.

In model extraction attacks, adversaries can steal a machine learning model exposed via a public API by repeatedly querying it and adjusting their own model based on obtained predictions. To prevent model stealing, existing defenses focus on detecting malicious queries, truncating, or distorting outputs, thus necessarily introducing a tradeoff between robustness and model utility for legitimate users. Instead, we propose to impede model extraction by requiring users to complete a proof-of-work before they can read the model's predictions. This deters attackers by greatly increasing (even up to 100x) the computational effort needed to leverage query access for model extraction. Since we calibrate the effort required to complete the proof-of-work to each query, this only introduces a slight overhead for regular users (up to 2x). To achieve this, our calibration applies tools from differential privacy to measure the information revealed by a query. Our method requires no modification of the victim model and can be applied by machine learning practitioners to guard their publicly exposed models against being easily stolen.

With the rapid increase of large-scale, real-world datasets, it becomes critical to address the problem of long-tailed data distribution (i.e., a few classes account for most of the data, while most classes are under-represented). Existing solutions typically adopt class re-balancing strategies such as re-sampling and re-weighting based on the number of observations for each class. In this work, we argue that as the number of samples increases, the additional benefit of a newly added data point will diminish. We introduce a novel theoretical framework to measure data overlap by associating with each sample a small neighboring region rather than a single point. The effective number of samples is defined as the volume of samples and can be calculated by a simple formula $(1-\beta^{n})/(1-\beta)$, where $n$ is the number of samples and $\beta \in [0,1)$ is a hyperparameter. We design a re-weighting scheme that uses the effective number of samples for each class to re-balance the loss, thereby yielding a class-balanced loss. Comprehensive experiments are conducted on artificially induced long-tailed CIFAR datasets and large-scale datasets including ImageNet and iNaturalist. Our results show that when trained with the proposed class-balanced loss, the network is able to achieve significant performance gains on long-tailed datasets.