Progress within physical oceanography has been concurrent with the increasing sophistication of tools available for its study. The incorporation of machine learning (ML) techniques offers exciting possibilities for advancing the capacity and speed of established methods and also for making substantial and serendipitous discoveries. Beyond vast amounts of complex data ubiquitous in many modern scientific fields, the study of the ocean poses a combination of unique challenges that ML can help address. The observational data available is largely spatially sparse, limited to the surface, and with few time series spanning more than a handful of decades. Important timescales span seconds to millennia, with strong scale interactions and numerical modelling efforts complicated by details such as coastlines. This review covers the current scientific insight offered by applying ML and points to where there is imminent potential. We cover the main three branches of the field: observations, theory, and numerical modelling. Highlighting both challenges and opportunities, we discuss both the historical context and salient ML tools. We focus on the use of ML in situ sampling and satellite observations, and the extent to which ML applications can advance theoretical oceanographic exploration, as well as aid numerical simulations. Applications that are also covered include model error and bias correction and current and potential use within data assimilation. While not without risk, there is great interest in the potential benefits of oceanographic ML applications; this review caters to this interest within the research community.

Spatial data is a rich source of information for actuarial applications: knowledge of a risk's location could improve an insurance company's ratemaking, reserving or risk management processes. Insurance companies with high exposures in a territory typically have a competitive advantage since they may use historical losses in a region to model spatial risk non-parametrically. Relying on geographic losses is problematic for areas where past loss data is unavailable. This paper presents a method based on data (instead of smoothing historical insurance claim losses) to construct a geographic ratemaking model. In particular, we construct spatial features within a complex representation model, then use the features as inputs to a simpler predictive model (like a generalized linear model). Our approach generates predictions with smaller bias and smaller variance than other spatial interpolation models such as bivariate splines in most situations. This method also enables us to generate rates in territories with no historical experience.

We define infinitesimal gradient boosting as a limit of the popular tree-based gradient boosting algorithm from machine learning. The limit is considered in the vanishing-learning-rate asymptotic, that is when the learning rate tends to zero and the number of gradient trees is rescaled accordingly. For this purpose, we introduce a new class of randomized regression trees bridging totally randomized trees and Extra Trees and using a softmax distribution for binary splitting. Our main result is the convergence of the associated stochastic algorithm and the characterization of the limiting procedure as the unique solution of a nonlinear ordinary differential equation in a infinite dimensional function space. Infinitesimal gradient boosting defines a smooth path in the space of continuous functions along which the training error decreases, the residuals remain centered and the total variation is well controlled.

To minimize the average of a set of log-convex functions, the stochastic Newton method iteratively updates its estimate using subsampled versions of the full objective's gradient and Hessian. We contextualize this optimization problem as sequential Bayesian inference on a latent state-space model with a discriminatively-specified observation process. Applying Bayesian filtering then yields a novel optimization algorithm that considers the entire history of gradients and Hessians when forming an update. We establish matrix-based conditions under which the effect of older observations diminishes over time, in a manner analogous to Polyak's heavy ball momentum. We illustrate various aspects of our approach with an example and review other relevant innovations for the stochastic Newton method.

Algorithms produce a growing portion of decisions and recommendations both in policy and business. Such algorithmic decisions are natural experiments (conditionally quasi-randomly assigned instruments) since the algorithms make decisions based only on observable input variables. We use this observation to develop a treatment-effect estimator for a class of stochastic and deterministic algorithms. Our estimator is shown to be consistent and asymptotically normal for well-defined causal effects. A key special case of our estimator is a high-dimensional regression discontinuity design. The proofs use tools from differential geometry and geometric measure theory, which may be of independent interest. The practical performance of our method is first demonstrated in a high-dimensional simulation resembling decision-making by machine learning algorithms. Our estimator has smaller mean squared errors compared to alternative estimators. We finally apply our estimator to evaluate the effect of Coronavirus Aid, Relief, and Economic Security (CARES) Act, where more than \$10 billion worth of relief funding is allocated to hospitals via an algorithmic rule. The estimates suggest that the relief funding has little effects on COVID-19-related hospital activity levels. Naive OLS and IV estimates exhibit substantial selection bias.

As we gain access to a greater depth and range of health-related information about individuals, three questions arise: (1) Can we build better models to predict individual-level risk of ill health? (2) How much data do we need to effectively predict ill health? (3) Are new methods required to process the added complexity that new forms of data bring? The aim of the study is to apply a machine learning approach to identify the relative contribution of personal, social, health-related, biomarker and genetic data as predictors of future health in individuals. Using longitudinal data from 6830 individuals in the UK from Understanding Society (2010-12 to 2015-17), the study compares the predictive performance of five types of measures: personal (e.g. age, sex), social (e.g. occupation, education), health-related (e.g. body weight, grip strength), biomarker (e.g. cholesterol, hormones) and genetic single nucleotide polymorphisms (SNPs). The predicted outcome variable was limiting long-term illness one and five years from baseline. Two machine learning approaches were used to build predictive models: deep learning via neural networks and XGBoost (gradient boosting decision trees). Model fit was compared to traditional logistic regression models. Results found that health-related measures had the strongest prediction of future health status, with genetic data performing poorly. Machine learning models only offered marginal improvements in model accuracy when compared to logistic regression models, but also performed well on other metrics e.g. neural networks were best on AUC and XGBoost on precision. The study suggests that increasing complexity of data and methods does not necessarily translate to improved understanding of the determinants of health or performance of predictive models of ill health.

The Bluetooth sensor embedded in mobile phones provides an unobtrusive, continuous, and cost-efficient means to capture individuals' proximity information, such as the nearby Bluetooth devices count (NBDC). The continuous NBDC data can partially reflect individuals' behaviors and status, such as social connections and interactions, working status, mobility, and social isolation and loneliness, which were found to be significantly associated with depression by previous survey-based studies. This paper aims to explore the NBDC data's value in predicting depressive symptom severity as measured via the 8-item Patient Health Questionnaire (PHQ-8). The data used in this paper included 2,886 bi-weekly PHQ-8 records collected from 316 participants recruited from three study sites in the Netherlands, Spain, and the UK as part of the EU RADAR-CNS study. From the NBDC data two weeks prior to each PHQ-8 score, we extracted 49 Bluetooth features, including statistical features and nonlinear features for measuring periodicity and regularity of individuals' life rhythms. Linear mixed-effect models were used to explore associations between Bluetooth features and the PHQ-8 score. We then applied hierarchical Bayesian linear regression models to predict the PHQ-8 score from the extracted Bluetooth features. A number of significant associations were found between Bluetooth features and depressive symptom severity. Compared with commonly used machine learning models, the proposed hierarchical Bayesian linear regression model achieved the best prediction metrics, R2= 0.526, and root mean squared error (RMSE) of 3.891. Bluetooth features can explain an extra 18.8% of the variance in the PHQ-8 score relative to the baseline model without Bluetooth features (R2=0.338, RMSE = 4.547).

We present a framework that allows for the non-asymptotic study of the $2$-Wasserstein distance between the invariant distribution of an ergodic stochastic differential equation and the distribution of its numerical approximation in the strongly log-concave case. This allows us to study in a unified way a number of different integrators proposed in the literature for the overdamped and underdamped Langevin dynamics. In addition, we analyse a novel splitting method for the underdamped Langevin dynamics which only requires one gradient evaluation per time step. Under an additional smoothness assumption on a $d$--dimensional strongly log-concave distribution with condition number $\kappa$, the algorithm is shown to produce with an $\mathcal{O}\big(\kappa^{5/4} d^{1/4}\epsilon^{-1/2} \big)$ complexity samples from a distribution that, in Wasserstein distance, is at most $\epsilon>0$ away from the target distribution.

Federated learning involves a central processor that works with multiple agents to find a global model. The process consists of repeatedly exchanging estimates, which results in the diffusion of information pertaining to the local private data. Such a scheme can be inconvenient when dealing with sensitive data, and therefore, there is a need for the privatization of the algorithms. Furthermore, the current architecture of a server connected to multiple clients is highly sensitive to communication failures and computational overloads at the server. Thus in this work, we develop a private multi-server federated learning scheme, which we call graph federated learning. We use cryptographic and differential privacy concepts to privatize the federated learning algorithm that we extend to the graph structure. We study the effect of privatization on the performance of the learning algorithm for general private schemes that can be modeled as additive noise. We show under convexity and Lipschitz conditions, that the privatized process matches the performance of the non-private algorithm, even when we increase the noise variance.

The laborious process of labeling data often bottlenecks projects that aim to leverage the power of supervised machine learning. Active Learning (AL) has been established as a technique to ameliorate this condition through an iterative framework that queries a human annotator for labels of instances with the most uncertain class assignment. Via this mechanism, AL produces a binary classifier trained on less labeled data but with little, if any, loss in predictive performance. Despite its advantages, AL can have difficulty with class-imbalanced datasets and results in an inefficient labeling process. To address these drawbacks, we investigate our unsupervised instance selection (UNISEL) technique followed by a Random Forest (RF) classifier on 10 outlier detection datasets under low-label conditions. These results are compared to AL performed on the same datasets. Further, we investigate the combination of UNISEL and AL. Results indicate that UNISEL followed by an RF performs comparably to AL with an RF and that the combination of UNISEL and AL demonstrates superior performance. The practical implications of these findings in terms of time savings and generalizability afforded by UNISEL are discussed.