In this paper, we theoretically prove that gradient descent can find a global minimum for nonlinear deep neural networks of sizes commonly encountered in practice. The theory developed in this paper requires only the number of trainable parameters to increase linearly as the number of training samples increases. This allows the size of the deep neural networks to be several orders of magnitude smaller than that required by the previous theories. Moreover, we prove that the linear increase of the size of the network is the optimal rate and that it cannot be improved, except by a logarithmic factor. Furthermore, deep neural networks with the trainability guarantee are shown to generalize well to unseen test samples with a natural dataset but not a random dataset.

Evaluating novel contextual bandit policies using logged data is crucial in applications where exploration is costly, such as medicine. But it usually relies on the assumption of no unobserved confounders, which is bound to fail in practice. We study the question of policy evaluation when we instead have proxies for the latent confounders and develop an importance weighting method that avoids fitting a latent outcome regression model. We show that unlike the unconfounded case no single set of weights can give unbiased evaluation for all outcome models, yet we propose a new algorithm that can still provably guarantee consistency by instead minimizing an adversarial balance objective. We further develop tractable algorithms for optimizing this objective and demonstrate empirically the power of our method when confounders are latent.

--Malaria is a life-threatening disease affecting millions. Microscopy-based assessment of thin blood films is a standard method to (i) determine malaria species and (ii) quanti-tate high-parasitemia infections. Full automation of malaria microscopy by machine learning (ML) is a challenging task because field-prepared slides vary widely in quality and presentation, and artifacts often heavily outnumber relatively rare parasites. In this work, we describe a complete, fully-automated framework for thin film malaria analysis that applies ML methods, including convolutional neural nets (CNNs), trained on a large and diverse dataset of field-prepared thin blood films. Quanti-tation and species identification results are close to sufficiently accurate for the concrete needs of drug resistance monitoring and clinical use-cases on field-prepared samples. We focus our methods and our performance metrics on the field use-case requirements. We discuss key issues and important metrics for the application of ML methods to malaria microscopy. Index T erms --malaria, automated microscopy, deep neural networks, gradient boosted trees I. I NTRODUCTION Malaria is a mosquito-borne disease caused by Plasmodium species ( P . Manual microscopy examination of Giemsa-stained blood films is a widespread malaria diagnosis method. Key use-cases include diagnosis; species identification (ID) to guide treatment [2]; and quantitation of parasites for drug resistance studies, to track how fast a drug clears parasites from the blood. However, a lack of training, high inter-sample variability in preparation and presentation, and difficult field conditions can result in poor accuracy [3], [4]. Also, lack of trained personnel limits the number of drug resistance sentinel sites. Malaria microscopy is a difficult task for automated image-processing and machine learning (ML) systems for two reasons: Field-prepared blood films vary widely in quality and presentation; and parasites are small (with feature size close to optical limits of resolution), rare, highly variable, and easily confused with non-parasite objects (artifacts). But it is also a high-value target, due to the potential benefit for so many people, and also because automated systems have some concrete advantages: They can be widely deployed, solving the expert-training bottleneck; they can examine more blood volume per patient, reducing variability in quantitation caused by Poisson statistics; and their results are reproducible.

Some Developments in Clustering Analysis on Stochastic Processes Qidi Peng Nan Rao † Ran Zhao ‡ Abstract We review some developments on clustering stochastic processes and come with the conclusion that asymptotically consistent clustering algorithms can be obtained when the processes are ergodic and the dissimilarity measure satisfies the triangle inequality. Examples are provided when the processes are distribution ergodic, covariance ergodic and locally asymptotically self-similar, respectively. Keywords: stochastic process, unsupervised clustering, stationary ergodic processes, local asymptotic self-similarity 1 Introduction A stochastic process is an infinite sequence of random variables indexed by "time". The time indexes can be either discrete or continuous. Stochastic process type data have been broadly explored in biological and medical research (Damian et al., 2007; Zhao et al., 2014; J a askinen et al., 2014; et al., 2018).

The Rashomon effect occurs when many different explanations exist for the same phenomenon. In machine learning, Leo Breiman used this term to describe problems where many accurate-but-different models exist to describe the same data. In this work, we study how the Rashomon effect can be useful for understanding the relationship between training and test performance, and the possibility that simple-yet-accurate models exist for many problems. We introduce the Rashomon set as the set of almost-equally-accurate models for a given problem, and study its properties and the types of models it could contain. We present the Rashomon ratio as a new measure related to simplicity of model classes, which is the ratio of the volume of the set of accurate models to the volume of the hypothesis space; the Rashomon ratio is different from standard complexity measures from statistical learning theory. For a hierarchy of hypothesis spaces, the Rashomon ratio can help modelers to navigate the trade-off between simplicity and accuracy in a surprising way. In particular, we find empirically that a plot of empirical risk vs. Rashomon ratio forms a characteristic $\Gamma$-shaped Rashomon curve, whose elbow seems to be a reliable model selection criterion. When the Rashomon set is large, models that are accurate - but that also have various other useful properties - can often be obtained. These models might obey various constraints such as interpretability, fairness, monotonicity, and computational benefits.

We provide larger step-size restrictions for which gradient descent based algorithms (almost surely) avoid strict saddle points. In particular, consider a twice differentiable (non-convex) objective function whose gradient has Lipschitz constant L and whose Hessian is well-behaved. We prove that the probability of initial conditions for gradient descent with step-size up to 2/L converging to a strict saddle point, given one uniformly random initialization, is zero. This extends previous results up to the sharp limit imposed by the convex case. In addition, the arguments hold in the case when a learning rate schedule is given, with either a continuous decaying rate or a piece-wise constant schedule.

Deep generative modelling using flows has gained popularity owing to the tractable exact log-likelihood estimation with efficient training and synthesis process. Trained flow models carry rich information about the structure and local variance in input data. However, a bottleneck for flow models to scale with increasing dimensions is that the latent space has same size as the high-dimensional input space. In this paper, we propose methods to reduce the latent space dimension of flow models. Our first approach includes replacing standard high dimensional prior with a learned prior from a low dimensional noise space. Further improving to achieve exact log-likelihood with reduced dimensionality, our second approach presents an improved multi-scale architecture (Dinh et al., 2016) via likelihood contribution based factorization of dimensions. Using our method over state-of-the-art flow models, we demonstrate improvements in log-likelihood score on standard image benchmarks. Our work ventures a data dependent factorization scheme which is more efficient than static counterparts in prior works.

The paper presents Imbalance-XGBoost, a Python package that combines the powerful XGBoost software with weighted and focal losses to tackle binary label-imbalanced classification tasks. Though a small-scale program in terms of size, the package is, to the best of the authors' knowledge, the first of its kind which provides an integrated implementation for the two losses on XGBoost and brings a general-purpose extension on XGBoost for label-imbalanced scenarios. In this paper, the design and usage of the package are described with exemplar code listings, and its convenience to be integrated into Python-driven Machine Learning projects is illustrated. Furthermore, as the first- and second-order derivatives of the loss functions are essential for the implementations, the algebraic derivation is discussed and it can be deemed as a separate algorithmic contribution. The performances of the algorithms implemented in the package are empirically evaluated on Parkinson's disease classification data set, and multiple state-of-the-art performances have been observed. Given the scalable nature of XGBoost, the package has great potentials to be applied to real-life binary classification tasks, which are usually of large-scale and label-imbalanced.

Quantum algorithms can enhance machine learning in different aspects. Here, we study quantum-enhanced least-square support vector machine (LS-SVM). Firstly, a novel quantum algorithm that uses continuous variable to assist matrix inversion is introduced to simplify the algorithm for quantum LS-SVM, while retaining exponential speed-up. Secondly, we propose a hybrid quantum-classical version for sparse solutions of LS-SVM. By encoding a large dataset into a quantum state, a much smaller transformed dataset can be extracted using quantum matrix toolbox, which is further processed in classical SVM. We also incorporate kernel methods into the above quantum algorithms, which uses both exponential growth Hilbert space of qubits and infinite dimensionality of continuous variable for quantum feature maps. The quantum LS-SVM exploits quantum properties to explore important themes for SVM such as sparsity and kernel methods, and stresses its quantum advantages ranging from speed-up to the potential capacity to solve classically difficult machine learning tasks.

Learning from triplet comparison data has been extensively studied in the context of metric learning, where we want to learn a distance metric between two instances, and ordinal embedding, where we want to learn an embedding in an Euclidean space of the given instances that preserves the comparison order as well as possible. Unlike fully-labeled data, triplet comparison data can be collected in a more accurate and human-friendly way. Although learning from triplet comparison data has been considered in many applications, an important fundamental question of whether we can learn a classifier only from triplet comparison data has remained unanswered. In this paper, we give a positive answer to this important question by proposing an unbiased estimator for the classification risk under the empirical risk minimization framework. Since the proposed method is based on the empirical risk minimization framework, it inherently has the advantage that any surrogate loss function and any model, including neural networks, can be easily applied. Furthermore, we theoretically establish an estimation error bound for the proposed empirical risk minimizer. Finally, we provide experimental results to show that our method empirically works well and outperforms various baseline methods.