Traditionally, spline or kernel approaches in combination with parametric estimation are used to infer the linear coefficient (fixed effects) in a partially linear mixed-effects model for repeated measurements. Using machine learning algorithms allows us to incorporate complex interaction structures and high-dimensional variables. We employ double machine learning to cope with the nonparametric part of the partially linear mixed-effects model: the nonlinear variables are regressed out nonparametrically from both the linear variables and the response. This adjustment can be performed with any machine learning algorithm, for instance random forests, which allows to take complex interaction terms and nonsmooth structures into account. The adjusted variables satisfy a linear mixed-effects model, where the linear coefficient can be estimated with standard linear mixed-effects techniques. We prove that the estimated fixed effects coefficient converges at the parametric rate, is asymptotically Gaussian distributed, and semiparametrically efficient. Two simulation studies demonstrate that our method outperforms a penalized regression spline approach in terms of coverage. We also illustrate our proposed approach on a longitudinal dataset with HIV-infected individuals. Software code for our method is available in the R-package dmlalg.
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We investigate optimal execution problems with instantaneous price impact and stochastic resilience. First, in the setting of linear price impact function we derive a closed-form recursion for the optimal strategy, generalizing previous results with deterministic transient price impact. Second, we develop a numerical algorithm for the case of nonlinear price impact. We utilize an actor-critic framework that constructs two neural-network surrogates for the value function and the feedback control. One advantage of such functional approximators is the ability to do parametric learning, i.e. to incorporate some of the model parameters as part of the input space. Precise calibration of price impact, resilience, etc., is known to be extremely challenging and hence it is critical to understand sensitivity of the strategy to these parameters. Our parametric neural network (NN) learner organically scales across 3-6 input dimensions and is shown to accurately approximate optimal strategy across a range of parameter configurations. We provide a fully reproducible Jupyter Notebook with our NN implementation, which is of independent pedagogical interest, demonstrating the ease of use of NN surrogates in (parametric) stochastic control problems.
Linear mixed models (LMMs) are instrumental for regression analysis with structured dependence, such as grouped, clustered, or multilevel data. However, selection among the covariates--while accounting for this structured dependence--remains a challenge. We introduce a Bayesian decision analysis for subset selection with LMMs. Using a Mahalanobis loss function that incorporates the structured dependence, we derive optimal linear coefficients for (i) any given subset of variables and (ii) all subsets of variables that satisfy a cardinality constraint. Crucially, these estimates inherit shrinkage or regularization and uncertainty quantification from the underlying Bayesian model, and apply for any well-specified Bayesian LMM. More broadly, our decision analysis strategy deemphasizes the role of a single "best" subset, which is often unstable and limited in its information content, and instead favors a collection of near-optimal subsets. This collection is summarized by key member subsets and variable-specific importance metrics. Customized subset search and out-of-sample approximation algorithms are provided for more scalable computing. These tools are applied to simulated data and a longitudinal physical activity dataset, and demonstrate excellent prediction, estimation, and selection ability.
In this work, we study the transfer learning problem under high-dimensional generalized linear models (GLMs), which aim to improve the fit on target data by borrowing information from useful source data. Given which sources to transfer, we propose a transfer learning algorithm on GLM, and derive its $\ell_1/\ell_2$-estimation error bounds as well as a bound for a prediction error measure. The theoretical analysis shows that when the target and source are sufficiently close to each other, these bounds could be improved over those of the classical penalized estimator using only target data under mild conditions. When we don't know which sources to transfer, an algorithm-free transferable source detection approach is introduced to detect informative sources. The detection consistency is proved under the high-dimensional GLM transfer learning setting. We also propose an algorithm to construct confidence intervals of each coefficient component, and the corresponding theories are provided. Extensive simulations and a real-data experiment verify the effectiveness of our algorithms. We implement the proposed GLM transfer learning algorithms in a new R package glmtrans, which is available on CRAN.
In this paper, we propose a PAC-Bayesian \textit{a posteriori} parameter selection scheme for adaptive regularized regression in Hilbert scales under general, unknown source conditions. We demonstrate that our approach is adaptive to misspecification, and achieves the optimal learning rate under subgaussian noise. Unlike existing parameter selection schemes, the computational complexity of our approach is independent of sample size. We derive minimax adaptive rates for a new, broad class of Tikhonov-regularized learning problems under general, misspecified source conditions, that notably do not require any conventional a priori assumptions on kernel eigendecay. Using the theory of interpolation, we demonstrate that the spectrum of the Mercer operator can be inferred in the presence of "tight" $L^{\infty}$ embeddings of suitable Hilbert scales. Finally, we prove, that under a $\Delta_2$ condition on the smoothness index functions, our PAC-Bayesian scheme can indeed achieve minimax rates. We discuss applications of our approach to statistical inverse problems and oracle-efficient contextual bandit algorithms.
We demonstrate that merely analog transmissions and match filtering can realize the function of an edge server in federated learning (FL). Therefore, a network with massively distributed user equipments (UEs) can achieve large-scale FL without an edge server. We also develop a training algorithm that allows UEs to continuously perform local computing without being interrupted by the global parameter uploading, which exploits the full potential of UEs' processing power. We derive convergence rates for the proposed schemes to quantify their training efficiency. The analyses reveal that when the interference obeys a Gaussian distribution, the proposed algorithm retrieves the convergence rate of a server-based FL. But if the interference distribution is heavy-tailed, then the heavier the tail, the slower the algorithm converges. Nonetheless, the system run time can be largely reduced by enabling computation in parallel with communication, whereas the gain is particularly pronounced when communication latency is high. These findings are corroborated via excessive simulations.
Blockchain and smart contract technology are novel approaches to data and code management that facilitate trusted computing by allowing for development in a distributed and decentralized manner. Testing smart contracts comes with its own set of challenges which have not yet been fully identified and explored. Although existing tools can identify and discover known vulnerabilities and their interactions on the Ethereum blockchain through random search or symbolic execution, these tools generally do not produce test suites suitable for human oracles. In this paper, we present AGSOLT (Automated Generator of Solidity Test Suites). We demonstrate its efficiency by implementing two search algorithms to automatically generate test suites for stand-alone Solidity smart contracts, taking into account some of the blockchain-specific challenges. To test AGSOLT, we compared a random search algorithm and a genetic algorithm on a set of 36 real-world smart contracts. We found that AGSOLT is capable of achieving high branch coverage with both approaches and even discovered some errors in some of the most popular Solidity smart contracts on Github.
Present-day atomistic simulations generate long trajectories of ever more complex systems. Analyzing these data, discovering metastable states, and uncovering their nature is becoming increasingly challenging. In this paper, we first use the variational approach to conformation dynamics to discover the slowest dynamical modes of the simulations. This allows the different metastable states of the system to be located and organized hierarchically. The physical descriptors that characterize metastable states are discovered by means of a machine learning method. We show in the cases of two proteins, Chignolin and Bovine Pancreatic Trypsin Inhibitor, how such analysis can be effortlessly performed in a matter of seconds. Another strength of our approach is that it can be applied to the analysis of both unbiased and biased simulations.
The adaptive processing of structured data is a long-standing research topic in machine learning that investigates how to automatically learn a mapping from a structured input to outputs of various nature. Recently, there has been an increasing interest in the adaptive processing of graphs, which led to the development of different neural network-based methodologies. In this thesis, we take a different route and develop a Bayesian Deep Learning framework for graph learning. The dissertation begins with a review of the principles over which most of the methods in the field are built, followed by a study on graph classification reproducibility issues. We then proceed to bridge the basic ideas of deep learning for graphs with the Bayesian world, by building our deep architectures in an incremental fashion. This framework allows us to consider graphs with discrete and continuous edge features, producing unsupervised embeddings rich enough to reach the state of the art on several classification tasks. Our approach is also amenable to a Bayesian nonparametric extension that automatizes the choice of almost all model's hyper-parameters. Two real-world applications demonstrate the efficacy of deep learning for graphs. The first concerns the prediction of information-theoretic quantities for molecular simulations with supervised neural models. After that, we exploit our Bayesian models to solve a malware-classification task while being robust to intra-procedural code obfuscation techniques. We conclude the dissertation with an attempt to blend the best of the neural and Bayesian worlds together. The resulting hybrid model is able to predict multimodal distributions conditioned on input graphs, with the consequent ability to model stochasticity and uncertainty better than most works. Overall, we aim to provide a Bayesian perspective into the articulated research field of deep learning for graphs.
The Bayesian paradigm has the potential to solve core issues of deep neural networks such as poor calibration and data inefficiency. Alas, scaling Bayesian inference to large weight spaces often requires restrictive approximations. In this work, we show that it suffices to perform inference over a small subset of model weights in order to obtain accurate predictive posteriors. The other weights are kept as point estimates. This subnetwork inference framework enables us to use expressive, otherwise intractable, posterior approximations over such subsets. In particular, we implement subnetwork linearized Laplace: We first obtain a MAP estimate of all weights and then infer a full-covariance Gaussian posterior over a subnetwork. We propose a subnetwork selection strategy that aims to maximally preserve the model's predictive uncertainty. Empirically, our approach is effective compared to ensembles and less expressive posterior approximations over full networks.
This paper focuses on the expected difference in borrower's repayment when there is a change in the lender's credit decisions. Classical estimators overlook the confounding effects and hence the estimation error can be magnificent. As such, we propose another approach to construct the estimators such that the error can be greatly reduced. The proposed estimators are shown to be unbiased, consistent, and robust through a combination of theoretical analysis and numerical testing. Moreover, we compare the power of estimating the causal quantities between the classical estimators and the proposed estimators. The comparison is tested across a wide range of models, including linear regression models, tree-based models, and neural network-based models, under different simulated datasets that exhibit different levels of causality, different degrees of nonlinearity, and different distributional properties. Most importantly, we apply our approaches to a large observational dataset provided by a global technology firm that operates in both the e-commerce and the lending business. We find that the relative reduction of estimation error is strikingly substantial if the causal effects are accounted for correctly.
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