Actin cytoskeleton networks generate local topological signatures due to the natural variations in the number, size, and shape of holes of the networks. Persistent homology is a method that explores these topological properties of data and summarizes them as persistence diagrams. In this work, we analyze and classify these filament networks by transforming them into persistence diagrams whose variability is quantified via a Bayesian framework on the space of persistence diagrams. The proposed generalized Bayesian framework adopts an independent and identically distributed cluster point process characterization of persistence diagrams and relies on a substitution likelihood argument. This framework provides the flexibility to estimate the posterior cardinality distribution of points in a persistence diagram and the posterior spatial distribution simultaneously. We present a closed form of the posteriors under the assumption of Gaussian mixtures and binomials for prior intensity and cardinality respectively. Using this posterior calculation, we implement a Bayes factor algorithm to classify the actin filament networks and benchmark it against several state-of-the-art classification methods.

In these applications, one often can only observe or use selected components of the data for decisionmaking due to the capacity limitation in data acquisition, transmission, processing, or storage. For instance, the sensor devices might have limited battery powers; thus, one might want to use a subset of sensors per time step over a long period instead of using full sensors simultaneously over a short period. Likewise, while sensing is usually cheap, the communication bandwidth is often limited from remote sensors to the fusion center that makes a global decision. The fusion center might prioritize certain local sensors to send local information for decision making. Also, in many applications such as quality engineering or biosurveillance, one faces the design issue and needs to decide which variables or patients to be measured to detect the defect or disease outbreak more efficiently. This paper aims to investigate how to efficiently real-time monitor high-dimensional streaming data under resource constraints.

The study focuses on extension to the approach of Principal Component Analysis (PCA), as defined in [1], [2] or [3]. PCA and related matrix factorisation methodologies are widely used in data-rich environments for dimensionality reduction, data compression, feature-extraction techniques or data de-noising. The methodologies identify a lower-dimensional linear subspace to represent the data, which captures second-order dominant information contained in high-dimensional data sets. PCA can be viewed as a matrix factorisation problem which aims to learn the lower-dimensional representation of the data, preserving its Euclidean structure. However, in the presence of either a non-Gaussian distribution of the data generating distribution or in the presence of outliers which corrupt the data, the standard PCA methodology provides biased information about the lower-rank representation. In many applications, the stochastic noise or observation errors in the data set are assumed to be, in some sense, "well-behaved"; for instance, additive, light-tailed, symmetric and zero-mean. When non-robust feature extraction methods are naively utilised in the presence of violations of these implicit statistical assumptions, the information contained in the extracted features cannot be relied upon, resulting in misleading inference. Therefore, it is critical to ensure that the feature extraction captures information about correct characteristics of the process generating the data. In the following study, we relax the inherent assumption of "well-behaved" observation noise by developing a class of robust estimators that can withstand violations of such assumptions, which routinely arise in real data sets.

Equipping machines with comprehensive knowledge of the world's entities and their relationships has been a long-standing goal of AI. Over the last decade, large-scale knowledge bases, also known as knowledge graphs, have been automatically constructed from web contents and text sources, and have become a key asset for search engines. This machine knowledge can be harnessed to semantically interpret textual phrases in news, social media and web tables, and contributes to question answering, natural language processing and data analytics. This article surveys fundamental concepts and practical methods for creating and curating large knowledge bases. It covers models and methods for discovering and canonicalizing entities and their semantic types and organizing them into clean taxonomies. On top of this, the article discusses the automatic extraction of entity-centric properties. To support the long-term life-cycle and the quality assurance of machine knowledge, the article presents methods for constructing open schemas and for knowledge curation. Case studies on academic projects and industrial knowledge graphs complement the survey of concepts and methods.

Precision medicine is a medical model, which proposes customization of the healthcare to a subgroup of patients, based on a genetics, lifestyle and environment. This technique allows doctors and researchers to prognosis treatment and prevention strategies for a specific disease which can work on a group of people. It is opposed to a one-size-fits-all approach, in which disease treatment and prevention techniques are advanced for the average individual with much less attention for the variations among individuals. There is an overlap between the terms "precision medication" and "personalized medicine." As per the National Research Council, "personalized medicine" is a traditional word with a meaning close to "precision medication."

Representation learning has been proven to play an important role in the unprecedented success of machine learning models in numerous tasks, such as machine translation, face recognition and recommendation. The majority of existing representation learning approaches often require a large number of consistent and noise-free labels. However, due to various reasons such as budget constraints and privacy concerns, labels are very limited in many real-world scenarios. Directly applying standard representation learning approaches on small labeled data sets will easily run into over-fitting problems and lead to sub-optimal solutions. Even worse, in some domains such as education, the limited labels are usually annotated by multiple workers with diverse expertise, which yields noises and inconsistency in such crowdsourcing settings. In this paper, we propose a novel framework which aims to learn effective representations from limited data with crowdsourced labels. Specifically, we design a grouping based deep neural network to learn embeddings from a limited number of training samples and present a Bayesian confidence estimator to capture the inconsistency among crowdsourced labels. Furthermore, to expedite the training process, we develop a hard example selection procedure to adaptively pick up training examples that are misclassified by the model. Extensive experiments conducted on three real-world data sets demonstrate the superiority of our framework on learning representations from limited data with crowdsourced labels, comparing with various state-of-the-art baselines. In addition, we provide a comprehensive analysis on each of the main components of our proposed framework and also introduce the promising results it achieved in our real production to fully understand the proposed framework.

Constrained Markov Decision Processes (CMDPs) formalize sequential decision-making problems whose objective is to minimize a cost function while satisfying constraints on various cost functions. In this paper, we consider the setting of episodic fixed-horizon CMDPs. We propose an online algorithm which leverages the linear programming formulation of finitehorizon CMDP for repeated optimistic planning to provide a probably approximately correct (PAC) guarantee on the number of episodes needed to ensure an ǫ-optimal policy, i.e., with resulting objective value within ǫ of the optimal value and satisfying the constraints within ǫ-tolerance, with probability at least 1 δ. S, the number of episodes needed have a linear dependence on the state and action space sizes S and A, respectively, and quadratic dependence on the time horizon H. Markov decision processes (MDPs) [1] offer a natural framework to express sequential decision-making problems and reason about autonomous system behaviors. However, the single cost objective of a traditional MDP formulation may fall short of fully capturing problems with multiple conflicting objectives and additional constraints that must be satisfied.

The problem of monotone missing data has been broadly studied during the last two decades and has many applications in different fields such as bioinformatics or statistics. Commonly used imputation techniques require multiple iterations through the data before yielding convergence. Moreover, those approaches may introduce extra noises and biases to the subsequent modeling. In this work, we derive exact formulas and propose a novel algorithm to compute the maximum likelihood estimators (MLEs) of a multiple class, monotone missing dataset when all the covariance matrices of all categories are assumed to be equal, namely EPEM. We then illustrate an application of our proposed methods in Linear Discriminant Analysis (LDA). As the computation is exact, our EPEM algorithm does not require multiple iterations through the data as other imputation approaches, thus promising to handle much less time-consuming than other methods. This effectiveness was validated by empirical results when EPEM reduced the error rates significantly and required a short computation time compared to several imputation-based approaches. We also release all codes and data of our experiments in one GitHub repository to contribute to the research community related to this problem.

Extreme multi-label classification (XMLC) is a learning task of tagging instances with a small subset of relevant labels chosen from an extremely large pool of possible labels. Problems of this scale can be efficiently handled by organizing labels as a tree, like in hierarchical softmax used for multi-class problems. In this paper, we thoroughly investigate probabilistic label trees (PLTs) which can be treated as a generalization of hierarchical softmax for multi-label problems. We first introduce the PLT model and discuss training and inference procedures and their computational costs. Next, we prove the consistency of PLTs for a wide spectrum of performance metrics. To this end, we upperbound their regret by a function of surrogate-loss regrets of node classifiers. Furthermore, we consider a problem of training PLTs in a fully online setting, without any prior knowledge of training instances, their features, or labels. In this case, both node classifiers and the tree structure are trained online. We prove a specific equivalence between the fully online algorithm and an algorithm with a tree structure given in advance. Finally, we discuss several implementations of PLTs and introduce a new one, napkinXC, which we empirically evaluate and compare with state-of-the-art algorithms.

Machine learning can be used to make sense of healthcare data. Probabilistic machine learning models help provide a complete picture of observed data in healthcare. In this review, we examine how probabilistic machine learning can advance healthcare. We consider challenges in the predictive model building pipeline where probabilistic models can be beneficial including calibration and missing data. Beyond predictive models, we also investigate the utility of probabilistic machine learning models in phenotyping, in generative models for clinical use cases, and in reinforcement learning.