In model serving, having one fixed model during the entire often life-long inference process is usually detrimental to model performance, as data distribution evolves over time, resulting in lack of reliability of the model trained on historical data. It is important to detect changes and retrain the model in time. The existing methods generally have three weaknesses: 1) using only classification error rate as signal, 2) assuming ground truth labels are immediately available after features from samples are received and 3) unable to decide what data to use to retrain the model when change occurs. We address the first problem by utilizing six different signals to capture a wide range of characteristics of data, and we address the second problem by allowing lag of labels, where labels of corresponding features are received after a lag in time. For the third problem, our proposed method automatically decides what data to use to retrain based on the signals. Extensive experiments on structured and unstructured data for different type of data changes establish that our method consistently outperforms the state-of-the-art methods by a large margin.

Deep Gaussian processes (DGPs) are increasingly popular as predictive models in machine learning (ML) for their non-stationary flexibility and ability to cope with abrupt regime changes in training data. Here we explore DGPs as surrogates for computer simulation experiments whose response surfaces exhibit similar characteristics. In particular, we transport a DGP's automatic warping of the input space and full uncertainty quantification (UQ), via a novel elliptical slice sampling (ESS) Bayesian posterior inferential scheme, through to active learning (AL) strategies that distribute runs non-uniformly in the input space -- something an ordinary (stationary) GP could not do. Building up the design sequentially in this way allows smaller training sets, limiting both expensive evaluation of the simulator code and mitigating cubic costs of DGP inference. When training data sizes are kept small through careful acquisition, and with parsimonious layout of latent layers, the framework can be both effective and computationally tractable. Our methods are illustrated on simulation data and two real computer experiments of varying input dimensionality. We provide an open source implementation in the "deepgp" package on CRAN.

How sensitive should machine learning models be to input changes? We tackle the question of model smoothness and show that it is a useful inductive bias which aids generalization, adversarial robustness, generative modeling and reinforcement learning. We explore current methods of imposing smoothness constraints and observe they lack the flexibility to adapt to new tasks, they don't account for data modalities, they interact with losses, architectures and optimization in ways not yet fully understood. We conclude that new advances in the field are hinging on finding ways to incorporate data, tasks and learning into our definitions of smoothness.

Conditional Value-at-Risk ($\mathrm{CV@R}$) is one of the most popular measures of risk, which has been recently considered as a performance criterion in supervised statistical learning, as it is related to desirable operational features in modern applications, such as safety, fairness, distributional robustness, and prediction error stability. However, due to its variational definition, $\mathrm{CV@R}$ is commonly believed to result in difficult optimization problems, even for smooth and strongly convex loss functions. We disprove this statement by establishing noisy (i.e., fixed-accuracy) linear convergence of stochastic gradient descent for sequential $\mathrm{CV@R}$ learning, for a large class of not necessarily strongly-convex (or even convex) loss functions satisfying a set-restricted Polyak-Lojasiewicz inequality. This class contains all smooth and strongly convex losses, confirming that classical problems, such as linear least squares regression, can be solved efficiently under the $\mathrm{CV@R}$ criterion, just as their risk-neutral versions. Our results are illustrated numerically on such a risk-aware ridge regression task, also verifying their validity in practice.

We study scalable alternatives to robust gradient descent (RGD) techniques that can be used when the losses and/or gradients can be heavy-tailed, though this will be unknown to the learner. The core technique is simple: instead of trying to robustly aggregate gradients at each step, which is costly and leads to sub-optimal dimension dependence in risk bounds, we instead focus computational effort on robustly choosing (or newly constructing) a strong candidate based on a collection of cheap stochastic sub-processes which can be run in parallel. The exact selection process depends on the convexity of the underlying objective, but in all cases, our selection technique amounts to a robust form of boosting the confidence of weak learners. In addition to formal guarantees, we also provide empirical analysis of robustness to perturbations to experimental conditions, under both sub-Gaussian and heavy-tailed data, along with applications to a variety of benchmark datasets. The overall take-away is an extensible procedure that is simple to implement, trivial to parallelize, which keeps the formal merits of RGD methods but scales much better to large learning problems.

This paper considers the problem of computing Bayesian estimates of both states and model parameters for nonlinear state-space models. Generally, this problem does not have a tractable solution and approximations must be utilised. In this work, a variational approach is used to provide an assumed density which approximates the desired, intractable, distribution. The approach is deterministic and results in an optimisation problem of a standard form. Due to the parametrisation of the assumed density selected first- and second-order derivatives are readily available which allows for efficient solutions. The proposed method is compared against state-of-the-art Hamiltonian Monte Carlo in two numerical examples.

For multimode processes, one has to establish local monitoring models corresponding to local modes. However, the significant features of previous modes may be catastrophically forgotten when a monitoring model for the current mode is built. It would result in an abrupt performance decrease. Is it possible to make local monitoring model remember the features of previous modes? Choosing the principal component analysis (PCA) as a basic monitoring model, we try to resolve this problem. A modified PCA algorithm is built with continual learning ability for monitoring multimode processes, which adopts elastic weight consolidation (EWC) to overcome catastrophic forgetting of PCA for successive modes. It is called PCA-EWC, where the significant features of previous modes are preserved when a PCA model is established for the current mode. The computational complexity and key parameters are discussed to further understand the relationship between PCA and the proposed algorithm. Numerical case study and a practical industrial system in China are employed to illustrate the effectiveness of the proposed algorithm.

AEGIS study possesses unique information on longitudinal changes in circulating glucose through continuous glucose monitoring technology (CGM). However, as usual in longitudinal medical studies, there is a significant amount of missing data in the outcome variables. For example, 40 percent of glycosylated hemoglobin (A1C) biomarker data are missing five years ahead. With the purpose to reduce the impact of this issue, this article proposes a new data analysis framework based on learning in reproducing kernel Hilbert spaces (RKHS) with missing responses that allows to capture non-linear relations between variable studies in different supervised modeling tasks. First, we extend the Hilbert-Schmidt dependence measure to test statistical independence in this context introducing a new bootstrap procedure, for which we prove consistency. Next, we adapt or use existing models of variable selection, regression, and conformal inference to obtain new clinical findings about glucose changes five years ahead with the AEGIS data. The most relevant findings are summarized below: i) We identify new factors associated with long-term glucose evolution; ii) We show the clinical sensibility of CGM data to detect changes in glucose metabolism; iii) We can improve clinical interventions based on our algorithms' expected glucose changes according to patients' baseline characteristics.

Motivated by a large number of applications ranging from sports to the automotive industry and healthcare, there is a great interest in modeling observation entities in the form of a sequence of possibly vector-valued measurements, recorded intermittently at several discrete points in time. Functional data analysis (FDA) considers such data as being values on the realizations of a stochastic process, recorded with some error, at discrete random times. The purpose of FDA is to study such trajectories, also called curves or functions. See, e.g., [37, 49, 21, 54, 19] for some recent references. The amount of such data collected grows rapidly as does the cost of their labeling. Thus, there is an increasing interest in methods that aim to identify homogeneous groups within functional datasets.

This paper studies some asymptotic properties of adaptive algorithms widely used in optimization and machine learning, and among them Adagrad and Rmsprop, which are involved in most of the blackbox deep learning algorithms. Our setup is the non-convex landscape optimization point of view, we consider a one time scale parametrization and we consider the situation where these algorithms may be used or not with mini-batches. We adopt the point of view of stochastic algorithms and establish the almost sure convergence of these methods when using a decreasing step-size point of view towards the set of critical points of the target function. With a mild extra assumption on the noise, we also obtain the convergence towards the set of minimizer of the function. Along our study, we also obtain a "convergence rate" of the methods, in the vein of the works of \cite{GhadimiLan}.