Continuous, ubiquitous monitoring through wearable sensors has the potential to collect useful information about users' context. Heart rate is an important physiologic measure used in a wide variety of applications, such as fitness tracking and health monitoring. However, wearable sensors that monitor heart rate, such as smartwatches and electrocardiogram (ECG) patches, can have gaps in their data streams because of technical issues (e.g., bad wireless channels, battery depletion, etc.) or user-related reasons (e.g. motion artifacts, user compliance, etc.). The ability to use other available sensor data (e.g., smartphone data) to estimate missing heart rate readings is useful to cope with any such gaps, thus improving data quality and continuity. In this paper, we test the feasibility of estimating raw heart rate using smartphone sensor data. Using data generated by 12 participants in a one-week study period, we were able to build both personalized and generalized models using regression, SVM, and random forest algorithms. All three algorithms outperformed the baseline moving-average interpolation method for both personalized and generalized settings. Moreover, our findings suggest that personalized models outperformed the generalized models, which speaks to the importance of considering personal physiology, behavior, and life style in the estimation of heart rate. The promising results provide preliminary evidence of the feasibility of combining smartphone sensor data with wearable sensor data for continuous heart rate monitoring.

We present a general method for fitting finite mixture models (FMM). Learning in a mixture model consists of finding the most likely cluster assignment for each data-point, as well as finding the parameters of the clusters themselves. In many mixture models, this is difficult with current learning methods, where the most common approach is to employ monotone learning algorithms e.g. the conventional expectation-maximisation algorithm. While effective, the success of any monotone algorithm is crucially dependant on good parameter initialisation, where a common choice is $K$-means initialisation, commonly employed for Gaussian mixture models. For other types of mixture models, the path to good initialisation parameters is often unclear and may require a problem-specific solution. To this end, we propose a general heuristic learning algorithm that utilises Boltzmann exploration to assign each observation to a specific base distribution within the mixture model, which we call Boltzmann exploration expectation-maximisation (BEEM). With BEEM, hard assignments allow straight forward parameter learning for each base distribution by conditioning only on its assigned observations. Consequently, it can be applied to mixtures of any base distribution where single component parameter learning is tractable. The stochastic learning procedure is able to escape local optima and is thus insensitive to parameter initialisation. We show competitive performance on a number of synthetic benchmark cases as well as on real-world datasets.

However, there are several practical considerations in the choice of meta-learning algorithm which can influence the computational efficiency and overall performance of MOCA. For the experiments in this paper, we leverage two meta-learning algorithms which offer a clean Bayesian learning interpretation, relatively low-dimensional posterior statistics, recursive updates for these statistics, and computationally efficient likelihood evaluation under the posterior predictive. For regression experiments, we use ALPaCA (Harrison et al., 2018); for classification experiments, we use a novel algorithm based on similar Bayesian updates which we refer to as PCOC, for probabilistic clustering for online classification. For completeness, we offer a high level overview of these algorithms and show how they fit into the MOCA framework in the following subsections.

To restore the historical sea surface temperatures (SSTs) better, it is important to construct a good calibration model for the associated proxies. In this paper, we introduce a new model for alkenone (${\rm{U}}_{37}^{\rm{K}'}$) based on the heteroscedastic Gaussian process (GP) regression method. Our nonparametric approach not only deals with the variable pattern of noises over SSTs but also contains a Bayesian method of classifying potential outliers.

As the size of the dataset grows, the cost of performing the distance computations needed to implement a query can become prohibitive. A method often used to reduce this computational cost is quantization of the vector space and location-based encoding of the dataset vectors. These encodings can be used during query processing to find approximate nearest neighbors of the query point quickly. Search speed can be improved by using shorter codes, but shorter codes have higher quantization error, leading to degraded precision. In this work, we propose the Interleaved Composite Quantization (ICQ) which achieves fast similarity search without using shorter codes. In ICQ, a small subset of the code is used to approximate the distances, with complete codes being used only when necessary. Our method effectively reduces both code length and quantization error . Furthermore, ICQ is compatible with several recently proposed techniques for reducing quantization error and can be used in conjunction with these other techniques to improve results. W e confirm these claims and show strong empirical performance of ICQ using several synthetic and real-word datasets.

Identification of disease subtypes and corresponding biomarkers can substantially improve clinical diagnosis and treatment selection. Discovering these subtypes in noisy, high dimensional biomedical data is often impossible for humans and challenging for machines. We introduce a new approach to facilitate the discovery of disease subtypes: Instead of analyzing the original data, we train a diagnostic classifier (healthy vs. diseased) and extract instance-wise explanations for the classifier's decisions. The distribution of instances in the explanation space of our diagnostic classifier amplifies the different reasons for belonging to the same class - resulting in a representation that is uniquely useful for discovering latent subtypes. We compare our ability to recover subtypes via cluster analysis on model explanations to classical cluster analysis on the original data. In multiple datasets with known ground-truth subclasses, most compellingly on UK Biobank brain imaging data and transcriptome data from the Cancer Genome Atlas, we show that cluster analysis on model explanations substantially outperforms the classical approach. While we believe clustering in explanation space to be particularly valuable for inferring disease subtypes, the method is more general and applicable to any kind of sub-type identification.

Machine learning is a mature scientific field with lots of theoretical results, established algorithms and processes that address various supervised and unsupervised problems using the provided data. In theoretical research, such data is generated in a convenient way, or various methods are compared on standard benchmark problems - where data samples are represented as dense real-valued vectors of fixed and relatively low length. Practical applications represented by such standard datasets can successfully be solved by one of a myriad of existing machine learning methods and their implementations. However, the most impact of machine learning is currently in the big data field with the problems that are well explained in natural language ("Find malicious files", "Is that website safe to browse?") but are hard to encode numerically. Data samples in these problems have distinct features coming from a huge unordered set of possible features. Same approach can cover a frequent case of missing feature values [10, 28].

Box 1053 Blindern 0316 Oslo, Norway Abstract The Brier score is commonly used for evaluating probability predictions. In survival analysis, with right-censored observations of the event times, this score can be weighted by the inverse probability of censoring (IPCW) to retain its original interpretation. It is common practice to estimate the censoring distribution with the Kaplan-Meier estimator, even though it assumes that the censoring distribution is independent of the covariates. This paper discusses the general impact of the censoring estimates on the Brier score and shows that the estimation of the censoring distribution can be problematic. In particular, when the censoring times can be identified from the covariates, the IPCW score is no longer valid. For administratively censored data, where the potential censoring times are known for all individuals, we propose an alternative version of the Brier score. This administrative Brier score does not require estimation of the censoring distribution and is valid even if the censoring times can be identified from the covariates. Keywords: survival analysis, time-to-event-prediction, customer churn, inverse probability weighting, progressive type I censoring 1. Introduction Recently, there has been an increasing interest in combining machine learning methodology with survival analysis for improved time-to-event prediction. Also worth mentioning is the Random Survival Forest (Ishwaran et al., 2008) which makes decision trees based on the log-rank test and estimates the cumulative hazards with the Nelson-Aalen estimator. Although these methods are available for right-censored event times, a substantial part of the machine learning community is not familiar with survival analysis and might find it reasonable to instead apply binary classifiers for time-to-event prediction. In short, a binary classifier estimates the probability that an individual experience the event by time t, and can be fitted by disregarding individuals censored before that time. Arguably, the two most common evaluation criteria for survival predictions are the inverse probability of censoring weighted (IPCW) Brier score (Graf et al., 1999; Gerds and Schumacher, 2006) and different versions of the concordance index (Harrell Jr et al., 1982; Antolini et al., 2005; Uno et al., 2011; Gerds et al., 2013).

Submodularity is one of the most well-studied properties of problem classes in combinatorial optimization and many applications of machine learning and data mining, with strong implications for guaranteed optimization. In this thesis, we investigate the role of submodularity in provable non-convex optimization and validation of algorithms. A profound understanding which classes of functions can be tractably optimized remains a central challenge for non-convex optimization. By advancing the notion of submodularity to continuous domains (termed "continuous submodularity"), we characterize a class of generally non-convex and non-concave functions -- continuous submodular functions, and derive algorithms for approximately maximizing them with strong approximation guarantees. Meanwhile, continuous submodularity captures a wide spectrum of applications, ranging from revenue maximization with general marketing strategies, MAP inference for DPPs to mean field inference for probabilistic log-submodular models, which renders it as a valuable domain knowledge in optimizing this class of objectives. Validation of algorithms is an information-theoretic framework to investigate the robustness of algorithms to fluctuations in the input/observations and their generalization ability. We investigate various algorithms for one of the paradigmatic unconstrained submodular maximization problem: MaxCut. Due to submodularity of the MaxCut objective, we are able to present efficient approaches to calculate the algorithmic information content of MaxCut algorithms. The results provide insights into the robustness of different algorithmic techniques for MaxCut.

Many inferential and learning tasks can be accomplished efficiently by means of distributed optimization algorithms where the network topology plays a critical role in driving the local interactions among neighboring agents. There is a large body of literature examining the effect of the graph structure on the performance of optimization strategies. In this article, we examine the inverse problem and consider the reverse question: How much information does observing the behavior at the nodes convey about the underlying network structure used for optimization? Over large-scale networks, the difficulty of addressing such inverse questions (or problems) is compounded by the fact that usually only a limited portion of nodes can be probed, giving rise to a second important question: Despite the presence of several unobserved nodes, are partial and local observations still sufficient to discover the graph linking the probed nodes? The article surveys recent advances on this inverse learning problem and related questions. Examples of applications are provided to illustrate how the interplay between graph learning and distributed optimization arises in practice, e.g., in cognitive engineered systems such as distributed detection, or in other real-world problems such as the mechanism of opinion formation over social networks and the mechanism of coordination in biological networks. A unifying framework for examining the reconstruction error will be described, which allows to devise and examine various estimation strategies enabling successful graph learning. The relevance of specific network attributes, such as sparsity versus density of connections, and node degree concentration, is discussed in relation to the topology inference goal. It is shown how universal (i.e., data-driven) clustering algorithms can be exploited to solve the graph learning problem.