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Clustered federated Multitask learning is introduced as an efficient technique when data is unbalanced and distributed amongst clients in a non-independent and identically distributed manner. While a similarity metric can provide client groups with specialized models according to their data distribution, this process can be time-consuming because the server needs to capture all data distribution first from all clients to perform the correct clustering. Due to resource and time constraints at the network edge, only a fraction of devices {is} selected every round, necessitating the need for an efficient scheduling technique to address these issues. Thus, this paper introduces a two-phased client selection and scheduling approach to improve the convergence speed while capturing all data distributions. This approach ensures correct clustering and fairness between clients by leveraging bandwidth reuse for participants spent a longer time training their models and exploiting the heterogeneity in the devices to schedule the participants according to their delay. The server then performs the clustering depending on predetermined thresholds and stopping criteria. When a specified cluster approximates a stopping point, the server employs a greedy selection for that cluster by picking the devices with lower delay and better resources. The convergence analysis is provided, showing the relationship between the proposed scheduling approach and the convergence rate of the specialized models to obtain convergence bounds under non-i.i.d. data distribution. We carry out extensive simulations, and the results demonstrate that the proposed algorithms reduce training time and improve the convergence speed while equipping every user with a customized model tailored to its data distribution.

Bayesian Additive Regression Trees (BART) are a powerful semiparametric ensemble learning technique for modeling nonlinear regression functions. Although initially BART was proposed for predicting only continuous and binary response variables, over the years multiple extensions have emerged that are suitable for estimating a wider class of response variables (e.g. categorical and count data) in a multitude of application areas. In this paper we describe a Generalized framework for Bayesian trees and their additive ensembles where the response variable comes from an exponential family distribution and hence encompasses a majority of these variants of BART. We derive sufficient conditions on the response distribution, under which the posterior concentrates at a minimax rate, up to a logarithmic factor. In this regard our results provide theoretical justification for the empirical success of BART and its variants.

We propose a framework for Bayesian Likelihood-Free Inference (LFI) based on Generalized Bayesian Inference. To define the generalized posterior, we use Scoring Rules (SRs), which evaluate probabilistic models given an observation. In LFI, we can sample from the model but not evaluate the likelihood; for this reason, we employ SRs which admit unbiased empirical estimates. We use the Energy and the Kernel SRs, for which our posterior enjoys consistency in a well-specified setting and outlier robustness, but our general framework applies to other SRs. The straightforward way to perform posterior inference relies on pseudo-marginal Markov Chain Monte Carlo (MCMC). While this works satisfactorily for simple setups, it mixes poorly, which makes inference impossible when many observations are present. Hence, we employ stochastic-gradient (SG) MCMC methods, which are rejection-free and have thus no mixing issues. The targets of both sampling schemes only approximate our posterior, but the error vanishes as the number of model simulations at each MCMC step increases. In practice, SG-MCMC performs better than pseudo-marginal at a lower computational cost when both are applicable and scales to higher-dimensional setups. In our simulation studies, we compare with related approaches on standard benchmarks and a chaotic dynamical system from meteorology; for the latter, SG-MCMC allows us to infer the parameters of a neural network used to parametrize a part of the update equations of the dynamical system.

We propose a simple yet powerful extension of Bayesian Additive Regression Trees which we name Hierarchical Embedded BART (HE-BART). The model allows for random effects to be included at the terminal node level of a set of regression trees, making HE-BART a non-parametric alternative to mixed effects models which avoids the need for the user to specify the structure of the random effects in the model, whilst maintaining the prediction and uncertainty calibration properties of standard BART. Using simulated and real-world examples, we demonstrate that this new extension yields superior predictions for many of the standard mixed effects models' example data sets, and yet still provides consistent estimates of the random effect variances. In a future version of this paper, we outline its use in larger, more advanced data sets and structures.

Practitioners often use data from a randomized controlled trial to learn a treatment assignment policy that can be deployed on a target population. A recurring concern in doing so is that, even if the randomized trial was well-executed (i.e., internal validity holds), the study participants may not represent a random sample of the target population (i.e., external validity fails)--and this may lead to policies that perform suboptimally on the target population. We consider a model where observable attributes can impact sample selection probabilities arbitrarily but the effect of unobservable attributes is bounded by a constant, and we aim to learn policies with the best possible performance guarantees that hold under any sampling bias of this type. In particular, we derive the partial identification result for the worst-case welfare in the presence of sampling bias and show that the optimal max-min, max-min gain, and minimax regret policies depend on both the conditional average treatment effect (CATE) and the conditional value-at-risk (CVaR) of potential outcomes given covariates. To avoid finite-sample inefficiencies of plug-in estimates, we further provide an end-to-end procedure for learning the optimal max-min and max-min gain policies that does not require the separate estimation of nuisance parameters.

As the availability, size and complexity of data have increased in recent years, machine learning (ML) techniques have become popular for modeling. Predictions resulting from applying ML models are often used for inference, decision-making, and downstream applications. A crucial yet often overlooked aspect of ML is uncertainty quantification, which can significantly impact how predictions from models are used and interpreted. Extreme Gradient Boosting (XGBoost) is one of the most popular ML methods given its simple implementation, fast computation, and sequential learning, which make its predictions highly accurate compared to other methods. However, techniques for uncertainty determination in ML models such as XGBoost have not yet been universally agreed among its varying applications. We propose enhancements to XGBoost whereby a modified quantile regression is used as the objective function to estimate uncertainty (QXGBoost). Specifically, we included the Huber norm in the quantile regression model to construct a differentiable approximation to the quantile regression error function. This key step allows XGBoost, which uses a gradient-based optimization algorithm, to make probabilistic predictions efficiently. QXGBoost was applied to create 90\% prediction intervals for one simulated dataset and one real-world environmental dataset of measured traffic noise. Our proposed method had comparable or better performance than the uncertainty estimates generated for regular and quantile light gradient boosting. For both the simulated and traffic noise datasets, the overall performance of the prediction intervals from QXGBoost were better than other models based on coverage width-based criterion.

Causal inference is a critical research topic across many domains, such as statistics, computer science, education, public policy and economics, for decades. Nowadays, estimating causal effect from observational data has become an appealing research direction owing to the large amount of available data and low budget requirement, compared with randomized controlled trials. Embraced with the rapidly developed machine learning area, various causal effect estimation methods for observational data have sprung up. In this survey, we provide a comprehensive review of causal inference methods under the potential outcome framework, one of the well known causal inference framework. The methods are divided into two categories depending on whether they require all three assumptions of the potential outcome framework or not. For each category, both the traditional statistical methods and the recent machine learning enhanced methods are discussed and compared. The plausible applications of these methods are also presented, including the applications in advertising, recommendation, medicine and so on. Moreover, the commonly used benchmark datasets as well as the open-source codes are also summarized, which facilitate researchers and practitioners to explore, evaluate and apply the causal inference methods.

This paper surveys the machine learning literature and presents machine learning as optimization models. Such models can benefit from the advancement of numerical optimization techniques which have already played a distinctive role in several machine learning settings. Particularly, mathematical optimization models are presented for commonly used machine learning approaches for regression, classification, clustering, and deep neural networks as well new emerging applications in machine teaching and empirical model learning. The strengths and the shortcomings of these models are discussed and potential research directions are highlighted.

In this paper, we propose a conceptually simple and geometrically interpretable objective function, i.e. additive margin Softmax (AM-Softmax), for deep face verification. In general, the face verification task can be viewed as a metric learning problem, so learning large-margin face features whose intra-class variation is small and inter-class difference is large is of great importance in order to achieve good performance. Recently, Large-margin Softmax and Angular Softmax have been proposed to incorporate the angular margin in a multiplicative manner. In this work, we introduce a novel additive angular margin for the Softmax loss, which is intuitively appealing and more interpretable than the existing works. We also emphasize and discuss the importance of feature normalization in the paper. Most importantly, our experiments on LFW BLUFR and MegaFace show that our additive margin softmax loss consistently performs better than the current state-of-the-art methods using the same network architecture and training dataset. Our code has also been made available at //github.com/happynear/AMSoftmax