Analyzing large X-ray diffraction (XRD) datasets is a key step in high-throughput mapping of the compositional phase diagrams of combinatorial materials libraries. Optimizing and automating this task can help accelerate the process of discovery of materials with novel and desirable properties. Here, we report a new method for pattern analysis and phase extraction of XRD datasets. The method expands the Nonnegative Matrix Factorization method, which has been used previously to analyze such datasets, by combining it with custom clustering and cross-correlation algorithms. This new method is capable of robust determination of the number of basis patterns present in the data which, in turn, enables straightforward identification of any possible peak-shifted patterns. Peak-shifting arises due to continuous change in the lattice constants as a function of composition, and is ubiquitous in XRD datasets from composition spread libraries. Successful identification of the peak-shifted patterns allows proper quantification and classification of the basis XRD patterns, which is necessary in order to decipher the contribution of each unique single-phase structure to the multi-phase regions. The process can be utilized to determine accurately the compositional phase diagram of a system under study. The presented method is applied to one synthetic and one experimental dataset, and demonstrates robust accuracy and identification abilities.

Learning to optimize - the idea that we can learn from data algorithms that optimize a numerical criterion - has recently been at the heart of a growing number of research efforts. One of the most challenging issues within this approach is to learn a policy that is able to optimize over classes of functions that are fairly different from the ones that it was trained on. We propose a novel way of framing learning to optimize as a problem of learning a good navigation policy on a partially observable loss surface. To this end, we develop Rover Descent, a solution that allows us to learn a fairly broad optimization policy from training on a small set of prototypical two-dimensional surfaces that encompasses the classically hard cases such as valleys, plateaus, cliffs and saddles and by using strictly zero-order information. We show that, without having access to gradient or curvature information, we achieve state-of-the-art convergence speed on optimization problems not presented at training time such as the Rosenbrock function and other hard cases in two dimensions. We extend our framework to optimize over high dimensional landscapes, while still handling only two-dimensional local landscape information and show good preliminary results.

The popular cubic regularization (CR) method converges with first- and second-order optimality guarantee for nonconvex optimization, but encounters a high sample complexity issue for solving large-scale problems. Various sub-sampling variants of CR have been proposed to improve the sample complexity.In this paper, we propose a stochastic variance-reduced cubic-regularized (SVRC) Newton's method under both sampling with and without replacement schemes. We characterize the per-iteration sample complexity bounds which guarantee the same rate of convergence as that of CR for nonconvex optimization. Furthermore, our method achieves a total Hessian sample complexity of $\mathcal{O}(N^{8/11} \epsilon^{-3/2})$ and $\mathcal{O}(N^{3/4}\epsilon^{-3/2})$ respectively under sampling without and with replacement, which improve that of CR as well as other sub-sampling variant methods via the variance reduction scheme. Our result also suggests that sampling without replacement yields lower sample complexity than that of sampling with replacement. We further compare the practical performance of SVRC with other cubic regularization methods via experiments.

Echo state networks are powerful recurrent neural networks. However, they are often unstable and shaky, making the process of finding an good ESN for a specific dataset quite hard. Obtaining a superb accuracy by using the Echo State Network is a challenging task. We create, develop and implement a family of predictably optimal robust and stable ensemble of Echo State Networks via regularizing the training and perturbing the input. Furthermore, several distributions of weights have been tried based on the shape to see if the shape of the distribution has the impact for reducing the error. We found ESN can track in short term for most dataset, but it collapses in the long run. Short-term tracking with large size reservoir enables ESN to perform strikingly with superior prediction. Based on this scenario, we go a further step to aggregate many of ESNs into an ensemble to lower the variance and stabilize the system by stochastic replications and bootstrapping of input data.

A folded type model is developed for analyzing compositional data. The proposed model, which is based upon the $\alpha$-transformation for compositional data, provides a new and flexible class of distributions for modeling data defined on the simplex sample space. Despite its rather seemingly complex structure, employment of the EM algorithm guarantees efficient parameter estimation. The model is validated through simulation studies and examples which illustrate that the proposed model performs better in terms of capturing the data structure, when compared to the popular logistic normal distribution.

We establish connections between the problem of learning a two-layers neural network with good generalization error and tensor decomposition. We consider a model with input $\boldsymbol x \in \mathbb R^d$, $r$ hidden units with weights $\{\boldsymbol w_i\}_{1\le i \le r}$ and output $y\in \mathbb R$, i.e., $y=\sum_{i=1}^r \sigma(\left \langle \boldsymbol x, \boldsymbol w_i\right \rangle)$, where $\sigma$ denotes the activation function. First, we show that, if we cannot learn the weights $\{\boldsymbol w_i\}_{1\le i \le r}$ accurately, then the neural network does not generalize well. More specifically, the generalization error is close to that of a trivial predictor with access only to the norm of the input. This result holds for any activation function, and it requires that the weights are roughly isotropic and the input distribution is Gaussian, which is a typical assumption in the theoretical literature. Then, we show that the problem of learning the weights $\{\boldsymbol w_i\}_{1\le i \le r}$ is at least as hard as the problem of tensor decomposition. This result holds for any input distribution and assumes that the activation function is a polynomial whose degree is related to the order of the tensor to be decomposed. By putting everything together, we prove that learning a two-layers neural network that generalizes well is at least as hard as tensor decomposition. It has been observed that neural network models with more parameters than training samples often generalize well, even if the problem is highly underdetermined. This means that the learning algorithm does not estimate the weights accurately and yet is able to yield a good generalization error. This paper shows that such a phenomenon cannot occur when the input distribution is Gaussian and the weights are roughly isotropic. We also provide numerical evidence supporting our theoretical findings.

As the prevalence and everyday use of machine learning algorithms, along with our reliance on these algorithms grow dramatically, so do the efforts to attack and undermine these algorithms with malicious intent, resulting in a growing interest in adversarial machine learning. A number of approaches have been developed that can render a machine learning algorithm ineffective through poisoning or other types of attacks. Most attack algorithms typically use sophisticated optimization approaches, whose objective function is designed to cause maximum damage with respect to accuracy and performance of the algorithm with respect to some task. In this effort, we show that while such an objective function is indeed brutally effective in causing maximum damage on an embedded feature selection task, it often results in an attack mechanism that can be easily detected with an embarrassingly simple novelty or outlier detection algorithm. We then propose an equally simple yet elegant solution by adding a regularization term to the attacker's objective function that penalizes outlying attack points.

Clinical prognostic models derived from largescale healthcare data can inform critical diagnostic and therapeutic decisions. To enable off-theshelf usage of machine learning (ML) in prognostic research, we developed AUTOPROGNOSIS: a system for automating the design of predictive modeling pipelines tailored for clinical prognosis. AUTOPROGNOSIS optimizes ensembles of pipeline configurations efficiently using a novel batched Bayesian optimization (BO) algorithm that learns a low-dimensional decomposition of the pipelines high-dimensional hyperparameter space in concurrence with the BO procedure. This is achieved by modeling the pipelines performances as a black-box function with a Gaussian process prior, and modeling the similarities between the pipelines baseline algorithms via a sparse additive kernel with a Dirichlet prior. Meta-learning is used to warmstart BO with external data from similar patient cohorts by calibrating the priors using an algorithm that mimics the empirical Bayes method. The system automatically explains its predictions by presenting the clinicians with logical association rules that link patients features to predicted risk strata. We demonstrate the utility of AUTOPROGNOSIS using 10 major patient cohorts representing various aspects of cardiovascular patient care.

Deep neural networks are a powerful technique for learning complex functions from data. However, their appeal in real-world applications can be hindered by an inability to quantify the uncertainty of predictions. In this paper, the generation of prediction intervals (PI) for quantifying uncertainty in regression tasks is considered. It is axiomatic that high-quality PIs should be as narrow as possible, whilst capturing a specified portion of data. In this paper we derive a loss function directly from this high-quality principle that requires no distributional assumption. We show how its form derives from a likelihood principle, that it can be used with gradient descent, and that in ensembled form, model uncertainty is accounted for. This remedies limitations of a popular model developed on the same high-quality principle. Experiments are conducted on ten regression benchmark datasets. The proposed quality-driven (QD) method is shown to outperform current state-of-the-art uncertainty quantification methods, reducing average PI width by around 10%.

It is widely believed that the success of deep convolutional networks is based on progressively discarding uninformative variability about the input with respect to the problem at hand. This is supported empirically by the difficulty of recovering images from their hidden representations, in most commonly used network architectures. In this paper we show via a one-to-one mapping that this loss of information is not a necessary condition to learn representations that generalize well on complicated problems, such as ImageNet. Via a cascade of homeomorphic layers, we build thei -RevNet, a network that can be fully inverted up to the final projection onto the classes, i.e. no information is discarded. Building an invertible architecture is difficult, for one, because the local inversion is ill-conditioned, we overcome this by providing an explicit inverse. An analysis of i-RevNets learned representations suggests an alternative explanation for the success of deep networks by a progressive contraction and linear separation with depth. To shed light on the nature of the model learned by thei -RevNet we reconstruct linear interpolations between natural image representations. A CNN may be very effective in classifying images of all sorts (He et al., 2016; Krizhevsky et al., 2012), but the cascade of linear and nonlinear operators reveals little about the contribution of the internal representation to the classification. The learning process is characterized by a steady reduction of large amounts of uninformative variability in the images while simultaneously revealing the essence of the visual class.