Early hospital mortality prediction is critical as intensivists strive to make efficient medical decisions about the severely ill patients staying in intensive care units. As a result, various methods have been developed to address this problem based on clinical records. However, some of the laboratory test results are time-consuming and need to be processed. In this paper, we propose a novel method to predict mortality using features extracted from the heart signals of patients within the first hour of ICU admission. In order to predict the risk, quantitative features have been computed based on the heart rate signals of ICU patients. Each signal is described in terms of 12 statistical and signal-based features. The extracted features are fed into eight classifiers: decision tree, linear discriminant, logistic regression, support vector machine (SVM), random forest, boosted trees, Gaussian SVM, and K-nearest neighborhood (K-NN). To derive insight into the performance of the proposed method, several experiments have been conducted using the well-known clinical dataset named Medical Information Mart for Intensive Care III (MIMIC-III). The experimental results demonstrate the capability of the proposed method in terms of precision, recall, F1-score, and area under the receiver operating characteristic curve (AUC). The decision tree classifier satisfies both accuracy and interpretability better than the other classifiers, producing an F1-score and AUC equal to 0.91 and 0.93, respectively. It indicates that heart rate signals can be used for predicting mortality in patients in the ICU, achieving a comparable performance with existing predictions that rely on high dimensional features from clinical records which need to be processed and may contain missing information.

We introduce interactive structure learning, an abstract problem that encompasses many interactive learning tasks that have traditionally been studied in isolation, including active learning of binary classifiers, interactive clustering, interactive embedding, and active learning of structured output predictors. These problems include variants of both supervised and unsupervised tasks, and allow many different types of feedback, from binary labels to must-link/cannot-link constraints to similarity assessments to structured outputs. Despite these surface differences, they conform to a common template that allows them to be fruitfully unified. In interactive structure learning, there is a space of items X --for instance, an input space on which a classifier is to be learned, or points to cluster, or points to embed in a metric space--and the goal is to learn a structure on X, chosen from a family G. This set G could consist, for example, of all linear classifiers on X, or all hierarchical clusterings of X, or all knowledge graphs on X.

Bayesian optimization is the core technique behind the emergence of AutoML, which holds the promise of automatically searching for models and hyperparameters to make machine learning techniques more accessible. As such services are moving towards the cloud, we ask -- {\em When multiple AutoML users share the same computational infrastructure, how should we allocate resources to maximize the "global happiness" of all users?} We focus on GP-EI, one of the most popular algorithms for automatic model selection and hyperparameter tuning, and develop a novel multi-device, multi-tenant extension that is aware of \emph{multiple} computation devices and multiple users sharing the same set of computation devices. Theoretically, given $N$ users and $M$ devices, we obtain a regret bound of $O((\text{\bf {MIU}}(T,K) + M)\frac{N^2}{M})$, where $\text{\bf {MIU}}(T,K)$ refers to the maximal incremental uncertainty up to time $T$ for the covariance matrix $K$. Empirically, we evaluate our algorithm on two applications of automatic model selection, and show that our algorithm significantly outperforms the strategy of serving users independently. Moreover, when multiple computation devices are available, we achieve near-linear speedup when the number of users is much larger than the number of devices.

Cluster analysis is a fundamental tool for pattern discovery of complex heterogeneous data. Prevalent clustering methods mainly focus on vector or matrix-variate data and are not applicable to general-order tensors, which arise frequently in modern scientific and business applications. Moreover, there is a gap between statistical guarantees and computational efficiency for existing tensor clustering solutions due to the nature of their non-convex formulations. In this work, we bridge this gap by developing a provable convex formulation of tensor co-clustering. Our convex co-clustering (CoCo) estimator enjoys stability guarantees and is both computationally and storage efficient. We further establish a non-asymptotic error bound for the CoCo estimator, which reveals a surprising "blessing of dimensionality" phenomenon that does not exist in vector or matrix-variate cluster analysis. Our theoretical findings are supported by extensive simulated studies. Finally, we apply the CoCo estimator to the cluster analysis of advertisement click tensor data from a major online company. Our clustering results provide meaningful business insights to improve advertising effectiveness.

We consider the problem of estimating the discrete clustering structures under Sub-Gaussian Mixture Models. Our main results establish a hidden integrality property of a semidefinite programming (SDP) relaxation for this problem: while the optimal solutions to the SDP are not integer-valued in general, their estimation errors can be upper bounded in terms of the error of an idealized integer program. The error of the integer program, and hence that of the SDP, are further shown to decay exponentially in the signal-to-noise ratio. To the best of our knowledge, this is the first exponentially decaying error bound for convex relaxations of mixture models, and our results reveal the "global-to-local" mechanism that drives the performance of the SDP relaxation. A corollary of our results shows that in certain regimes the SDP solutions are in fact integral and exact, improving on existing exact recovery results for convex relaxations. More generally, our results establish sufficient conditions for the SDP to correctly recover the cluster memberships of $(1-\delta)$ fraction of the points for any $\delta\in(0,1)$. As a special case, we show that under the $d$-dimensional Stochastic Ball Model, SDP achieves non-trivial (sometimes exact) recovery when the center separation is as small as $\sqrt{1/d}$, which complements previous exact recovery results that require constant separation.

Split-Merge MCMC (Monte Carlo Markov Chain) is one of the essential and popular variants of MCMC for problems when an MCMC state consists of an unknown number of components. It is well known that state-of-the-art methods for split-merge MCMC do not scale well. Strategies for rapid mixing requires smart and informative proposals to reduce the rejection rate. However, all known smart proposals involve expensive operations to suggest informative transitions. As a result, the cost of each iteration is prohibitive for massive scale datasets. It is further known that uninformative but computationally efficient proposals, such as random split-merge, leads to extremely slow convergence. This tradeoff between mixing time and per update cost seems hard to get around. In this paper, we get around this tradeoff by utilizing simple similarity information, such as cosine similarity, between the entity vectors to design a proposal distribution. Such information is readily available in almost all applications. We show that the recent use of locality sensitive hashing for efficient adaptive sampling can be leveraged to obtain a computationally efficient pseudo-marginal MCMC. The new split-merge MCMC has cheap proposal which is also informative and needs significantly fewer iterations than random split-merge. Overall, we obtain a sweet tradeoff between convergence and per update cost. As a direct consequence, our proposal, named LSHSM, is around 5x faster than the state-of-the-art sampling methods on both synthetic datasets and two large real datasets KDDCUP and PubMed with several millions of entities and thousands of clusters.

Manifold learning based methods have been widely used for non-linear dimensionality reduction (NLDR). However, in many practical settings, the need to process streaming data is a challenge for such methods, owing to the high computational complexity involved. Moreover, most methods operate under the assumption that the input data is sampled from a single manifold, embedded in a high dimensional space. We propose a method for streaming NLDR when the observed data is either sampled from multiple manifolds or irregularly sampled from a single manifold. We show that existing NLDR methods, such as Isomap, fail in such situations, primarily because they rely on smoothness and continuity of the underlying manifold, which is violated in the scenarios explored in this paper. However, the proposed algorithm is able to learn effectively in presence of multiple, and potentially intersecting, manifolds, while allowing for the input data to arrive as a massive stream.

Python is a great programming language for data analysis. Scikit Learn is one of the scikit packages and its a very easy to use Machine learning package. It implements many machine learning algorithms and all you need to know is which algorithm solves your problem. We will use linear regression model. It is the easiest algorithm to start with – you have a function f(x) y, you have some pairs of (x,y) that match the function and you want to predict y for other x values.

Injecting adversarial examples during training, known as adversarial training, can improve robustness against one-step attacks, but not for unknown iterative attacks. To address this challenge, we first show iteratively generated adversarial images easily transfer between networks trained with the same strategy. Inspired by this observation, we propose cascade adversarial training, which transfers the knowledge of the end results of adversarial training. We train a network from scratch by injecting iteratively generated adversarial images crafted from already defended networks in addition to one-step adversarial images from the network being trained. We also propose to utilize embedding space for both classification and low-level (pixel-level) similarity learning to ignore unknown pixel level perturbation. During training, we inject adversarial images without replacing their corresponding clean images and penalize the distance between the two embeddings (clean and adversarial). Experimental results show that cascade adversarial training together with our proposed low-level similarity learning efficiently enhances the robustness against iterative attacks, but at the expense of decreased robustness against one-step attacks. We show that combining those two techniques can also improve robustness under the worst case black box attack scenario.

Markov decision processes (MDPs) (Bellman, 1957; Puterman, 2014) are the primary mathematical model for representing sequential decision problems with an indefinite time horizon (Bertsekas and Tsitsiklis, 1996; Sutton and Barto, 1998; Bather, 2000; Si, 2004; Powell, 2007; Wiering and Van Otterlo, 2012). This class of models is quite general as almost any decision process can be made into an MDP by concatenating data over multiple decision points (see Section 2 for a precise statement); however, coercing a decision process into the MDP framework in this way can lead to high-dimensional system state information that is difficult to model effectively. One common approach to construct a low-dimensional decision process from a high-dimensional MDP is to create a finite discretization of the space of possible system states and to treat the resultant process as a finite MDP (Gordon, 1995; Murao and Kitamura, 1997; Sutton and Barto, 1998; Kamio et al., 2004; Whiteson et al., 2007). However, such discretization can result in a significant loss of information and can be difficult to apply when the system state information is continuous and high-dimensional. Another common approach to dimension reduction is to construct a low-dimensional summary of the underlying system states, e.g., by applying principal components analysis (Jolliffe, 1986), multidimensional scaling (Borg and Groenen, 1997), or by constructing a local linear embedding (Roweis and Saul, 2000).