Quick and accurate medical diagnosis is crucial for the successful treatment of a disease. Using machine learning algorithms, we have built two models to predict a hematologic disease, based on laboratory blood test results. In one predictive model, we used all available blood test parameters and in the other a reduced set, which is usually measured upon patient admittance. Both models produced good results, with a prediction accuracy of 0.88 and 0.86, when considering the list of five most probable diseases, and 0.59 and 0.57, when considering only the most probable disease. Models did not differ significantly from each other, which indicates that a reduced set of parameters contains a relevant fingerprint of a disease, expanding the utility of the model for general practitioner's use and indicating that there is more information in the blood test results than physicians recognize. In the clinical test we showed that the accuracy of our predictive models was on a par with the ability of hematology specialists. Our study is the first to show that a machine learning predictive model based on blood tests alone, can be successfully applied to predict hematologic diseases and could open up unprecedented possibilities in medical diagnosis.

Traditional Recurrent Neural Networks assume vectorized data as inputs. However many data from modern science and technology come in certain structures such as tensorial time series data. To apply the recurrent neural networks for this type of data, a vectorisation process is necessary, while such a vectorisation leads to the loss of the precise information of the spatial or longitudinal dimensions. In addition, such a vectorized data is not an optimum solution for learning the representation of the longitudinal data. In this paper, we propose a new variant of tensorial neural networks which directly take tensorial time series data as inputs. We call this new variant as Tensorial Recurrent Neural Network (TRNN). The proposed TRNN is based on tensor Tucker decomposition.

Tensor train (TT) decomposition provides a space-efficient representation for higher-order tensors. Despite its advantage, we face two crucial limitations when we apply the TT decomposition to machine learning problems: the lack of statistical theory and of scalable algorithms. In this paper, we address the limitations. First, we introduce a convex relaxation of the TT decomposition problem and derive its error bound for the tensor completion task. Next, we develop an alternating optimization method with a randomization technique, in which the time complexity is as efficient as the space complexity is. In experiments, we numerically confirm the derived bounds and empirically demonstrate the performance of our method with a real higher-order tensor.

The study of networks leads to a wide range of high dimensional inference problems. In most practical scenarios, one needs to draw inference from a small population of large networks. The present paper studies hypothesis testing of graphs in this high-dimensional regime. We consider the problem of testing between two populations of inhomogeneous random graphs defined on the same set of vertices. We propose tests based on estimates of the Frobenius and operator norms of the difference between the population adjacency matrices. We show that the tests are uniformly consistent in both the "large graph, small sample" and "small graph, large sample" regimes. We further derive lower bounds on the minimax separation rate for the associated testing problems, and show that the constructed tests are near optimal.

In this paper we study the problem of learning Rectified Linear Units (ReLUs) which are functions of the form $max(0,)$ with $w$ denoting the weight vector. We study this problem in the high-dimensional regime where the number of observations are fewer than the dimension of the weight vector. We assume that the weight vector belongs to some closed set (convex or nonconvex) which captures known side-information about its structure. We focus on the realizable model where the inputs are chosen i.i.d.~from a Gaussian distribution and the labels are generated according to a planted weight vector. We show that projected gradient descent, when initialization at 0, converges at a linear rate to the planted model with a number of samples that is optimal up to numerical constants. Our results on the dynamics of convergence of these very shallow neural nets may provide some insights towards understanding the dynamics of deeper architectures.

We provide a comprehensive study of the convergence of forward-backward algorithm under suitable geometric conditions leading to fast rates. We present several new results and collect in a unified view a variety of results scattered in the literature, often providing simplified proofs. Novel contributions include the analysis of infinite dimensional convex minimization problems, allowing the case where minimizers might not exist. Further, we analyze the relation between different geometric conditions, and discuss novel connections with a priori conditions in linear inverse problems, including source conditions, restricted isometry properties and partial smoothness.

Generative Adversarial Networks (GANs) [Goodfellow et al., 2014] have become one of the dominant methods for fitting generative models to complicated real-life data, and even found unusual uses such as designing good cryptographic primitives [Abadi and Andersen, 2016]. See a survey by Goodfellow [2016]. Various novel architectures and training objectives were introduced to address perceived shortcomings of the original idea, leading to more stable training and more realistic generative models in practice (see Odena et al. [2016], Huang et al. [2017], Radford et al. [2016], Tolstikhin et al. [2017], Salimans et al. [2016], Jiwoong Im et al. [2016], Durugkar et al. [2016] and the reference therein).

We study the problem of learning to choose from m discrete treatment options (e.g., news item or medical drug) the one with best causal effect for a particular instance (e.g., user or patient) where the training data consists of passive observations of covariates, treatment, and the outcome of the treatment. The standard approach to this problem is regress and compare: split the training data by treatment, fit a regression model in each split, and, for a new instance, predict all m outcomes and pick the best. By reformulating the problem as a single learning task rather than m separate ones, we propose a new approach based on recursively partitioning the data into regimes where different treatments are optimal. We extend this approach to an optimal partitioning approach that finds a globally optimal partition, achieving a compact, interpretable, and impactful personalization model. We develop new tools for validating and evaluating personalization models on observational data and use these to demonstrate the power of our novel approaches in a personalized medicine and a job training application.

We propose a generic Markov Chain Monte Carlo (MCMC) algorithm to speed up computations for datasets with many observations. A key feature of our approach is the use of the highly efficient difference estimator from the survey sampling literature to estimate the log-likelihood accurately using only a small fraction of the data. Our algorithm improves on the $O(n)$ complexity of regular MCMC by operating over local data clusters instead of the full sample when computing the likelihood. The likelihood estimate is used in a Pseudo-marginal framework to sample from a perturbed posterior which is within $O(m^{-1/2})$ of the true posterior, where $m$ is the subsample size. The method is applied to a logistic regression model to predict firm bankruptcy for a large data set. We document a significant speed up in comparison to the standard MCMC on the full dataset.

Using the previously developed concepts of semantic spacetime, I explore the interpretation of knowledge representations, and their structure, as a semantic system, within the framework of promise theory. By assigning interpretations to phenomena, from observers to observed, we may approach a simple description of knowledge-based functional systems, with direct practical utility. The focus is especially on the interpretation of concepts, associative knowledge, and context awareness. The inference seems to be that most if not all of these concepts emerge from purely semantic spacetime properties, which opens the possibility for a more generalized understanding of what constitutes a learning, or even `intelligent' system. Some key principles emerge for effective knowledge representation: 1) separation of spacetime scales, 2) the recurrence of four irreducible types of association, by which intent propagates: aggregation, causation, cooperation, and similarity, 3) the need for discrimination of identities (discrete), which is assisted by distinguishing timeline simultaneity from sequential events, and 4) the ability to learn (memory). It is at least plausible that emergent knowledge abstraction capabilities have their origin in basic spacetime structures. These notes present a unified view of mostly well-known results; they allow us to see information models, knowledge representations, machine learning, and semantic networking (transport and information base) in a common framework. The notion of `smart spaces' thus encompasses artificial systems as well as living systems, across many different scales, e.g. smart cities and organizations.