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In the context of the high-dimensional Gaussian linear regression for ordered variables, we study the variable selection procedure via the minimization of the penalized least-squares criterion. We focus on model selection where we propose to control predictive risk and False Discovery Rate simultaneously. For this purpose, we obtain a convenient trade-off thanks to a proper calibration of the hyperparameter K appearing in the penalty function. We obtain non-asymptotic theoretical bounds on the False Discovery Rate with respect to K. We then provide an algorithm for the calibration of K. It is based on completely observable quantities in view of applications. Our algorithm is validated by an extensive simulation study.

This paper studies a semiparametric quantile regression model with endogenous variables and random right censoring. The endogeneity issue is solved using instrumental variables. It is assumed that the structural quantile of the logarithm of the outcome variable is linear in the covariates and censoring is independent. The regressors and instruments can be either continuous or discrete. The specification generates a continuum of equations of which the quantile regression coefficients are a solution. Identification is obtained when this system of equations has a unique solution. Our estimation procedure solves an empirical analogue of the system of equations. We derive conditions under which the estimator is asymptotically normal and prove the validity of a bootstrap procedure for inference. The finite sample performance of the approach is evaluated through numerical simulations. An application to the national Job Training Partnership Act study illustrates the method.

Many real-world systems can be described by mathematical formulas that are human-comprehensible, easy to analyze and can be helpful in explaining the system's behaviour. Symbolic regression is a method that generates nonlinear models from data in the form of analytic expressions. Historically, symbolic regression has been predominantly realized using genetic programming, a method that iteratively evolves a population of candidate solutions that are sampled by genetic operators crossover and mutation. This gradient-free evolutionary approach suffers from several deficiencies: it does not scale well with the number of variables and samples in the training data, models tend to grow in size and complexity without an adequate accuracy gain, and it is hard to fine-tune the inner model coefficients using just genetic operators. Recently, neural networks have been applied to learn the whole analytic formula, i.e., its structure as well as the coefficients, by means of gradient-based optimization algorithms. We propose a novel neural network-based symbolic regression method that constructs physically plausible models based on limited training data and prior knowledge about the system. The method employs an adaptive weighting scheme to effectively deal with multiple loss function terms and an epoch-wise learning process to reduce the chance of getting stuck in poor local optima. Furthermore, we propose a parameter-free method for choosing the model with the best interpolation and extrapolation performance out of all models generated through the whole learning process. We experimentally evaluate the approach on the TurtleBot 2 mobile robot, the magnetic manipulation system, the equivalent resistance of two resistors in parallel, and the anti-lock braking system. The results clearly show the potential of the method to find sparse and accurate models that comply with the prior knowledge provided.

This manuscript considers the problem of learning a random Gaussian network function using a fully connected network with frozen intermediate layers and trainable readout layer. This problem can be seen as a natural generalization of the widely studied random features model to deeper architectures. First, we prove Gaussian universality of the test error in a ridge regression setting where the learner and target networks share the same intermediate layers, and provide a sharp asymptotic formula for it. Establishing this result requires proving a deterministic equivalent for traces of the deep random features sample covariance matrices which can be of independent interest. Second, we conjecture the asymptotic Gaussian universality of the test error in the more general setting of arbitrary convex losses and generic learner/target architectures. We provide extensive numerical evidence for this conjecture, which requires the derivation of closed-form expressions for the layer-wise post-activation population covariances. In light of our results, we investigate the interplay between architecture design and implicit regularization.

Predictive models -- as with machine learning -- can underpin causal inference, to estimate the effects of an intervention at the population or individual level. This opens the door to a plethora of models, useful to match the increasing complexity of health data, but also the Pandora box of model selection: which of these models yield the most valid causal estimates? Classic machine-learning cross-validation procedures are not directly applicable. Indeed, an appropriate selection procedure for causal inference should equally weight both outcome errors for each individual, treated or not treated, whereas one outcome may be seldom observed for a sub-population. We study how more elaborate risks benefit causal model selection. We show theoretically that simple risks are brittle to weak overlap between treated and non-treated individuals as well as to heterogeneous errors between populations. Rather a more elaborate metric, the R-risk appears as a proxy of the oracle error on causal estimates, observable at the cost of an overlap re-weighting. As the R-risk is defined not only from model predictions but also by using the conditional mean outcome and the treatment probability, using it for model selection requires adapting cross validation. Extensive experiments show that the resulting procedure gives the best causal model selection.

Neural architecture-based recommender systems have achieved tremendous success in recent years. However, when dealing with highly sparse data, they still fall short of expectation. Self-supervised learning (SSL), as an emerging technique to learn with unlabeled data, recently has drawn considerable attention in many fields. There is also a growing body of research proceeding towards applying SSL to recommendation for mitigating the data sparsity issue. In this survey, a timely and systematical review of the research efforts on self-supervised recommendation (SSR) is presented. Specifically, we propose an exclusive definition of SSR, on top of which we build a comprehensive taxonomy to divide existing SSR methods into four categories: contrastive, generative, predictive, and hybrid. For each category, the narrative unfolds along its concept and formulation, the involved methods, and its pros and cons. Meanwhile, to facilitate the development and evaluation of SSR models, we release an open-source library SELFRec, which incorporates multiple benchmark datasets and evaluation metrics, and has implemented a number of state-of-the-art SSR models for empirical comparison. Finally, we shed light on the limitations in the current research and outline the future research directions.

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.

Spatio-temporal representation learning is critical for video self-supervised representation. Recent approaches mainly use contrastive learning and pretext tasks. However, these approaches learn representation by discriminating sampled instances via feature similarity in the latent space while ignoring the intermediate state of the learned representations, which limits the overall performance. In this work, taking into account the degree of similarity of sampled instances as the intermediate state, we propose a novel pretext task - spatio-temporal overlap rate (STOR) prediction. It stems from the observation that humans are capable of discriminating the overlap rates of videos in space and time. This task encourages the model to discriminate the STOR of two generated samples to learn the representations. Moreover, we employ a joint optimization combining pretext tasks with contrastive learning to further enhance the spatio-temporal representation learning. We also study the mutual influence of each component in the proposed scheme. Extensive experiments demonstrate that our proposed STOR task can favor both contrastive learning and pretext tasks. The joint optimization scheme can significantly improve the spatio-temporal representation in video understanding. The code is available at //github.com/Katou2/CSTP.

Federated Learning (FL) is a decentralized machine-learning paradigm, in which a global server iteratively averages the model parameters of local users without accessing their data. User heterogeneity has imposed significant challenges to FL, which can incur drifted global models that are slow to converge. Knowledge Distillation has recently emerged to tackle this issue, by refining the server model using aggregated knowledge from heterogeneous users, other than directly averaging their model parameters. This approach, however, depends on a proxy dataset, making it impractical unless such a prerequisite is satisfied. Moreover, the ensemble knowledge is not fully utilized to guide local model learning, which may in turn affect the quality of the aggregated model. Inspired by the prior art, we propose a data-free knowledge distillation} approach to address heterogeneous FL, where the server learns a lightweight generator to ensemble user information in a data-free manner, which is then broadcasted to users, regulating local training using the learned knowledge as an inductive bias. Empirical studies powered by theoretical implications show that, our approach facilitates FL with better generalization performance using fewer communication rounds, compared with the state-of-the-art.

Transfer learning aims at improving the performance of target learners on target domains by transferring the knowledge contained in different but related source domains. In this way, the dependence on a large number of target domain data can be reduced for constructing target learners. Due to the wide application prospects, transfer learning has become a popular and promising area in machine learning. Although there are already some valuable and impressive surveys on transfer learning, these surveys introduce approaches in a relatively isolated way and lack the recent advances in transfer learning. As the rapid expansion of the transfer learning area, it is both necessary and challenging to comprehensively review the relevant studies. This survey attempts to connect and systematize the existing transfer learning researches, as well as to summarize and interpret the mechanisms and the strategies in a comprehensive way, which may help readers have a better understanding of the current research status and ideas. Different from previous surveys, this survey paper reviews over forty representative transfer learning approaches from the perspectives of data and model. The applications of transfer learning are also briefly introduced. In order to show the performance of different transfer learning models, twenty representative transfer learning models are used for experiments. The models are performed on three different datasets, i.e., Amazon Reviews, Reuters-21578, and Office-31. And the experimental results demonstrate the importance of selecting appropriate transfer learning models for different applications in practice.