We study the information content of nuclear masses from the perspective of global models of nuclear binding energies. To this end, we employ a number of statistical methods and diagnostic tools, including Bayesian calibration, Bayesian model averaging, chi-square correlation analysis, principal component analysis, and empirical coverage probability. Using Bayesian framework, we investigate the structure of the 4-parameter Liquid Drop Model by considering discrepant mass domains for calibration. We then use the chi-square correlation framework to analyze the 14-parameter Skyrme energy density functional calibrated using homogeneous and heterogeneous datasets. We show that a quite dramatic parameter reduction can be achieved in both cases. The advantage of the Bayesian model averaging for improving the uncertainty quantification is demonstrated. The statistical approaches used are pedagogically described; in this context this work can serve as a guide for future applications.

Data corruption, systematic or adversarial, may skew statistical estimation severely. Recent work provides computationally efficient estimators that nearly match the information-theoretic optimal statistic. Yet the corruption model they consider measures sample-level corruption and is not fine-grained enough for many real-world applications. In this paper, we propose a coordinate-level metric of distribution shift over high-dimensional settings with n coordinates. We introduce and analyze robust mean estimation techniques against an adversary who may hide individual coordinates of samples while being bounded by that metric. We show that for structured distribution settings, methods that leverage structure to fill in missing entries before mean estimation can improve the estimation accuracy by a factor of approximately n compared to structure-agnostic methods. We also leverage recent progress in matrix completion to obtain estimators for recovering the true mean of the samples in settings of unknown structure. We demonstrate with real-world data that our methods can capture the dependencies across attributes and provide accurate mean estimation even in high-magnitude corruption settings.

Identifying when to give treatments to patients and how to select among multiple treatments over time are important medical problems with a few existing solutions. In this paper, we introduce the Counterfactual Recurrent Network (CRN), a novel sequence-to-sequence model that leverages the increasingly available patient observational data to estimate treatment effects over time and answer such medical questions. To handle the bias from time-varying confounders, covariates affecting the treatment assignment policy in the observational data, CRN uses domain adversarial training to build balancing representations of the patient history. At each timestep, CRN constructs a treatment invariant representation which removes the association between patient history and treatment assignments and thus can be reliably used for making counterfactual predictions. On a simulated model of tumour growth, with varying degree of time-dependent confounding, we show how our model achieves lower error in estimating counterfactuals and in choosing the correct treatment and timing of treatment than current state-of-the-art methods.

Stochastic gradient descent (SGD) algorithm is widely used for parameter estimation especially in online setting. While this recursive algorithm is popular for computation and memory efficiency, the problem of quantifying variability and randomness of the solutions has been rarely studied. This paper aims at conducting statistical inference of SGD-based estimates in online setting. In particular, we propose a fully online estimator for the covariance matrix of averaged SGD iterates (ASGD). Based on the classic asymptotic normality results of ASGD, we construct asymptotically valid confidence intervals for model parameters. Upon receiving new observations, we can quickly update the covariance estimator and confidence intervals. This approach fits in online setting even if the total number of data is unknown and takes the full advantage of SGD: efficiency in both computation and memory.

Given any increasing sequence of norms $\|\cdot\|_0,\dots,\|\cdot\|_{T-1}$, we provide an online convex optimization algorithm that outputs points $w_t$ in some domain $W$ in response to convex losses $\ell_t:W\to \mathbb{R}$ that guarantees regret $R_T(u)=\sum_{t=1}^T \ell_t(w_t)-\ell_t(u)\le \tilde O\left(\|u\|_{T-1}\sqrt{\sum_{t=1}^T \|g_t\|_{t-1,\star}^2}\right)$ where $g_t$ is a subgradient of $\ell_t$ at $w_t$. Our method does not require tuning to the value of $u$ and allows for arbitrary convex $W$. We apply this result to obtain new "full-matrix"-style regret bounds. Along the way, we provide a new examination of the full-matrix AdaGrad algorithm, suggesting a better learning rate value that improves significantly upon prior analysis. We use our new techniques to tune AdaGrad on-the-fly, realizing our improved bound in a concrete algorithm.

Data scientists have nowadays to deal with massive and complex datasets, that are often corrupted by outliers. Classical data mining procedures such as K-means or more general EM algorithms for instance are however sensitive to the presence of outliers, which can induce a time consuming pre-processing of the data. In this context, robust versions of data mining procedures are particularly relevant and we investigate a way to produce a Lloyd-type algorithm for hard clustering that is robust to the presence of ouliers. To do this, we propose to use a variant of median-of-means (MOM) statistics, that we call bootstrap median-of-means (bMOM). MOM principle has been the object of recent active research in mean estimation, regression, highdimensional framework and also supervised classification and machine learning ([17, 9, 15, 16, 19, 18, 20, 22]). Note that other approaches to robustness for K-means exist in the literature, such as for instance K-median or trimmed K-means (see for instance the survey [10] and references therein; see also [5]). Given a dataset, the boostrap median-of-means consists in first generating a (large) bootstrap sample and then perform a classical median-of-means on this bootstrap sample. We prove in Section 2 that if enough blocks are generated from the bootstrap sampling, then for a fixed block size, bMOM has a higher breakdown point than MOM.

The goal of this research project is to analyze the dynamics of social networks using machine learning techniques to locate maximal cliques and to find clusters for the purpose of identifying a target demographic. Unsupervised machine learning techniques are designed and implemented in this project to analyze a dataset from YouTube to discover communities in the social network and find central nodes. Different clustering algorithms are implemented and applied to the YouTube dataset. The well-known Bron-Kerbosch algorithm is used effectively in this research to find maximal cliques. The results obtained from this research could be used for advertising purposes and for building smart recommendation systems. All algorithms were implemented using Python programming language. The experimental results show that we were able to successfully find central nodes through clique-centrality and degree centrality. By utilizing clique detection algorithms, the research shown how machine learning algorithms can detect close knit groups within a larger network.

Systems developed in wearable devices with sensors onboard are widely used to collect data of humans and animals activities with the perspective of an on-board automatic classification of data. An interesting application of these systems is to support animals' behaviour monitoring gathered by sensors' data analysis. This is a challenging area and in particular with fixed memories capabilities because the devices should be able to operate autonomously for long periods before being retrieved by human operators, and being able to classify activities onboard can significantly improve their autonomy. In this paper, we focus on the identification of prey handling activity in seals (when the animal start attaching and biting the prey), which is one of the main movement that identifies a successful foraging activity. Data taken into consideration are streams of 3D accelerometers and depth sensors values collected by devices attached directly on seals. To analyse these data, we propose an automatic model based on Machine Learning (ML) algorithms. In particular, we compare the performance (in terms of accuracy and F1score) of three ML algorithms: Input Delay Neural Networks, Support Vector Machines, and Echo State Networks. We attend to the final aim of developing an automatic classifier on-board. For this purpose, in this paper, the comparison is performed concerning the performance obtained by each ML approach developed and its memory footprint. In the end, we highlight the advantage of using an ML algorithm, in terms of feasibility in wild animals' monitoring.

Abstract--This paper focuses on learning rate analysis of distributed kernel ridge regression for strong mixing sequences. Index Terms--Distributed learning, strong mixing sequences, kernel ridge regression, learning rate. I. Introduction With the development of data mining, data of massive size are collected in numerous application regions including Figure 1: Training flow of distributed learning recommendable systems, medical analysis, search engineering, financial analysis, online text, sensor network monitoring and social activity mining. A. Distributed learning cannot be reflected by data of small size [9], and creating new Distributed learning is a natural and preferable approach growth opportunities to combine and analyze industry data [3]. Finally, these distributively stored data.

In min-min optimization or max-min optimization, one has to compute the gradient of a function defined as a minimum. In most cases, the minimum has no closed-form, and an approximation is obtained via an iterative algorithm. There are two usual ways of estimating the gradient of the function: using either an analytic formula obtained by assuming exactness of the approximation, or automatic differentiation through the algorithm. In this paper, we study the asymptotic error made by these estimators as a function of the optimization error. We find that the error of the automatic estimator is close to the square of the error of the analytic estimator, reflecting a super-efficiency phenomenon. The convergence of the automatic estimator greatly depends on the convergence of the Jacobian of the algorithm. We analyze it for gradient descent and stochastic gradient descent and derive convergence rates for the estimators in these cases. Our analysis is backed by numerical experiments on toy problems and on Wasserstein barycenter computation. Finally, we discuss the computational complexity of these estimators and give practical guidelines to chose between them.