Tests for Esophageal cancer can be expensive, uncomfortable and can have side effects. For many patients, we can predict non-existence of disease with 100% certainty, just using demographics, lifestyle, and medical history information. Our objective is to devise a general methodology for customizing tests using user preferences so that expensive or uncomfortable tests can be avoided. We propose to use classifiers trained from electronic health records (EHR) for selection of tests. The key idea is to design classifiers with 100% false normal rates, possibly at the cost higher false abnormals. We compare Naive Bayes classification (NB), Random Forests (RF), Support Vector Machines (SVM) and Logistic Regression (LR), and find kernel Logistic regression to be most suitable for the task. We propose an algorithm for finding the best probability threshold for kernel LR, based on test set accuracy. Using the proposed algorithm, we describe schemes for selecting tests, which appear as features in the automatic classification algorithm, using preferences on costs and discomfort of the users. We test our methodology with EHRs collected for more than 3000 patients, as a part of project carried out by a reputed hospital in Mumbai, India. Kernel SVM and kernel LR with a polynomial kernel of degree 3, yields an accuracy of 99.8% and sensitivity 100%, without the MP features, i.e. using only clinical tests. We demonstrate our test selection algorithm using two case studies, one using cost of clinical tests, and other using "discomfort" values for clinical tests. We compute the test sets corresponding to the lowest false abnormals for each criterion described above, using exhaustive enumeration of 15 clinical tests. The sets turn out to different, substantiating our claim that one can customize test sets based on user preferences.

Deep learning tools have gained tremendous attention in applied machine learning. However such tools for regression and classification do not capture model uncertainty. In comparison, Bayesian models offer a mathematically grounded framework to reason about model uncertainty, but usually come with a prohibitive computational cost. In this paper we develop a new theoretical framework casting dropout training in deep neural networks (NNs) as approximate Bayesian inference in deep Gaussian processes. A direct result of this theory gives us tools to model uncertainty with dropout NNs -- extracting information from existing models that has been thrown away so far. This mitigates the problem of representing uncertainty in deep learning without sacrificing either computational complexity or test accuracy. We perform an extensive study of the properties of dropout's uncertainty. Various network architectures and non-linearities are assessed on tasks of regression and classification, using MNIST as an example. We show a considerable improvement in predictive log-likelihood and RMSE compared to existing state-of-the-art methods, and finish by using dropout's uncertainty in deep reinforcement learning.

We consider a problem of data integration. Consider determining which genes affect a disease. The genes, which we call predictor objects, can be measured in different experiments on the same individual. We address the question of finding which genes are predictors of disease by any of the experiments. Our formulation is more general. In a given data set, there are a fixed number of responses for each individual, which may include a mix of discrete, binary and continuous variables. There is also a class of predictor objects, which may differ within a subject depending on how the predictor object is measured, i.e., depend on the experiment. The goal is to select which predictor objects affect any of the responses, where the number of such informative predictor objects or features tends to infinity as sample size increases. There are marginal likelihoods for each way the predictor object is measured, i.e., for each experiment. We specify a pseudolikelihood combining the marginal likelihoods, and propose a pseudolikelihood information criterion. Under regularity conditions, we establish selection consistency for the pseudolikelihood information criterion with unbounded true model size, which includes a Bayesian information criterion with appropriate penalty term as a special case. Simulations indicate that data integration improves upon, sometimes dramatically, using only one of the data sources.

Bayesian optimization has become a fundamental global optimization algorithm in many problems where sample efficiency is of paramount importance. Recently, there has been proposed a large number of new applications in fields such as robotics, machine learning, experimental design, simulation, etc. In this paper, we focus on several problems that appear in robotics and autonomous systems: algorithm tuning, automatic control and intelligent design. All those problems can be mapped to global optimization problems. However, they become hard optimization problems. Bayesian optimization internally uses a probabilistic surrogate model (e.g.: Gaussian process) to learn from the process and reduce the number of samples required. In order to generalize to unknown functions in a black-box fashion, the common assumption is that the underlying function can be modeled with a stationary process. Nonstationary Gaussian process regression cannot generalize easily and it typically requires prior knowledge of the function. Some works have designed techniques to generalize Bayesian optimization to nonstationary functions in an indirect way, but using techniques originally designed for regression, where the objective is to improve the quality of the surrogate model everywhere. Instead optimization should focus on improving the surrogate model near the optimum. In this paper, we present a novel kernel function specially designed for Bayesian optimization, that allows nonstationary behavior of the surrogate model in an adaptive local region. In our experiments, we found that this new kernel results in an improved local search (exploitation), without penalizing the global search (exploration). We provide results in well-known benchmarks and real applications. The new method outperforms the state of the art in Bayesian optimization both in stationary and nonstationary problems.

Bayesian networks (Pearl [13]) are convenient graphical expressions for high dimensional probability distributions representing complex relationships between a large number of random variables. A Bayesian network is a directed acyclic graph consisting of nodes which represent random variables and arrows which correspond to probabilistic dependencies between them. There has been a great deal of interest in recent years on the NPhard problem of learning the structure (placement of directed edges) of Bayesian networks from data ([1],[2],[4],[5], [6],[8],[9],[11],[12]). Much of this has been driven by the study of genetic regulatory networks in molecular biology due to advances in technology and, specifically, microarray techniques that allow scientists to rapidly measure expression levels of genes in cells. As an integral part of machine learning, Bayesian networks have also been used for pattern recognition, language processing including speech recognition, and credit risk analysis. Structure learning typically involves defining a network score function and is then, in theory, a straightforward optimization problem.

This paper begins with considering the identification of sparse linear time-invariant networks described by multivariable ARX models. Such models possess relatively simple structure thus used as a benchmark to promote further research. With identifiability of the network guaranteed, this paper presents an identification method that infers both the Boolean structure of the network and the internal dynamics between nodes. Identification is performed directly from data without any prior knowledge of the system, including its order. The proposed method solves the identification problem using Maximum a posteriori estimation (MAP) but with inseparable penalties for complexity, both in terms of element (order of nonzero connections) and group sparsity (network topology). Such an approach is widely applied in Compressive Sensing (CS) and known as Sparse Bayesian Learning (SBL). We then propose a novel scheme that combines sparse Bayesian and group sparse Bayesian to efficiently solve the problem. The resulted algorithm has a similar form of the standard Sparse Group Lasso (SGL) while with known noise variance, it simplifies to exact re-weighted SGL. The method and the developed toolbox can be applied to infer networks from a wide range of fields, including systems biology applications such as signaling and genetic regulatory networks.

Causal inference concerns the identification of cause-effect relationships between variables. However, often only linear combinations of variables constitute meaningful causal variables. For example, recovering the signal of a cortical source from electroencephalography requires a well-tuned combination of signals recorded at multiple electrodes. We recently introduced the MERLiN (Mixture Effect Recovery in Linear Networks) algorithm that is able to recover, from an observed linear mixture, a causal variable that is a linear effect of another given variable. Here we relax the assumption of this cause-effect relationship being linear and present an extended algorithm that can pick up non-linear cause-effect relationships. Thus, the main contribution is an algorithm (and ready to use code) that has broader applicability and allows for a richer model class. Furthermore, a comparative analysis indicates that the assumption of linear cause-effect relationships is not restrictive in analysing electroencephalographic data.

The empirical validation of community detection methods is often based on available annotations on the nodes that serve as putative indicators of the large-scale network structure. Most often, the suitability of the annotations as topological descriptors itself is not assessed, and without this it is not possible to ultimately distinguish between actual shortcomings of the community detection algorithms on one hand, and the incompleteness, inaccuracy or structured nature of the data annotations themselves on the other. In this work we present a principled method to access both aspects simultaneously. We construct a joint generative model for the data and metadata, and a nonparametric Bayesian framework to infer its parameters from annotated datasets. We assess the quality of the metadata not according to its direct alignment with the network communities, but rather in its capacity to predict the placement of edges in the network. We also show how this feature can be used to predict the connections to missing nodes when only the metadata is available, as well as missing metadata. By investigating a wide range of datasets, we show that while there are seldom exact agreements between metadata tokens and the inferred data groups, the metadata is often informative of the network structure nevertheless, and can improve the prediction of missing nodes. This shows that the method uncovers meaningful patterns in both the data and metadata, without requiring or expecting a perfect agreement between the two.

Recent contributions have framed linear system identification as a nonparametric regularized inverse problem. Relying on $\ell_2$-type regularization which accounts for the stability and smoothness of the impulse response to be estimated, these approaches have been shown to be competitive w.r.t classical parametric methods. In this paper, adopting Maximum Entropy arguments, we derive a new $\ell_2$ penalty deriving from a vector-valued kernel; to do so we exploit the structure of the Hankel matrix, thus controlling at the same time complexity, measured by the McMillan degree, stability and smoothness of the identified models. As a special case we recover the nuclear norm penalty on the squared block Hankel matrix. In contrast with previous literature on reweighted nuclear norm penalties, our kernel is described by a small number of hyper-parameters, which are iteratively updated through marginal likelihood maximization; constraining the structure of the kernel acts as a (hyper)regularizer which helps controlling the effective degrees of freedom of our estimator. To optimize the marginal likelihood we adapt a Scaled Gradient Projection (SGP) algorithm which is proved to be significantly computationally cheaper than other first and second order off-the-shelf optimization methods. The paper also contains an extensive comparison with many state-of-the-art methods on several Monte-Carlo studies, which confirms the effectiveness of our procedure.

Computed tomography (CT) equivalent information is needed for attenuation correction in PET imaging and for dose planning in radiotherapy. Prior work has shown that Gaussian mixture models can be used to generate a substitute CT (s-CT) image from a specific set of MRI modalities. This work introduces a more flexible class of mixture models for s-CT generation, that incorporates spatial dependency in the data through a Markov random field prior on the latent field of class memberships associated with a mixture model. Furthermore, the mixture distributions are extended from Gaussian to normal inverse Gaussian (NIG), allowing heavier tails and skewness. The amount of data needed to train a model for s-CT generation is of the order of 100 million voxels. The computational efficiency of the parameter estimation and prediction methods are hence paramount, especially when spatial dependency is included in the models. A stochastic Expectation Maximization (EM) gradient algorithm is proposed in order to tackle this challenge. The advantages of the spatial model and NIG distributions are evaluated with a cross-validation study based on data from 14 patients. The study show that the proposed model enhances the predictive quality of the s-CT images by reducing the mean absolute error with 17.9%. Also, the distribution of CT values conditioned on the MR images are better explained by the proposed model as evaluated using continuous ranked probability scores.