Gramatyka 10, 30-067 Krak ow, Poland Abstract --While we would like to predict exact values, available incomplete information is rarely sufficient - usually allowing only to predict conditional probability distributions. This article discusses hierarchical correlation reconstruction (HCR) methodology for such prediction on example of usually unavailable bid-ask spreads, predicted from more accessible data like closing price, volume, high/low price, returns. In HCR methodology we first normalize marginal distributions to nearly uniform like in copula theory. Then here we model each moment (separately) of predicted variable as a linear combination of mixed moments of known variables using least squares linear regression - getting accurate description with interpretable coefficients describing linear relations between moments. Combining such predicted moments we get predicted density as a polynomial, for which we can e.g. There were performed 10-fold cross-validation log-likelihood tests for 22 DAX companies, leading to very accurate predictions, especially when using individual models for each company as there were found large differences between their behaviors. Additional advantage of the discussed methodology is being computationally inexpensive, finding and evaluation a model with hundreds of parameters and thousands of data points takes a second on a laptop. I NTRODUCTION While it is more convenient to work on exact values, real life predictions usually have some uncertainty, controlling of which could allow e.g. to distinguish nearly certain predictions from the practically worthless ones. Generally, wanting to predict Y variable from X ( X 1,...,X d) variables, if there is no a strict relation, they often come from some complicated joint probability distribution - knowing X x, we can only predict Pr ( Y X x) conditional probability distribution.

We study the estimation of $f(\btheta)$ under Gaussian shift model $\bx = \btheta+\bxi$, where $\btheta \in \RR^d$ is an unknown parameter, $\bxi \sim \mathcal{N}(\mathbf{0},\bSigma)$ is the random noise with covariance matrix $\bSigma$, and $f$ is a given function which belongs to certain Besov space with smoothness index $s>1$. Let $\sigma^2 = \|\bSigma\|_{op}$ be the operator norm of $\bSigma$ and $\sigma^{-2\alpha} = \br(\bSigma)$ be its effective rank with some $0<\alpha<1$ and $\sigma>0$. We develop a new estimator $g(\bx)$ based on a Fourier analytical approach that achieves effective bias reduction. We show that when the intrinsic dimension of the problem is large enough such that nontrivial bias reduction is needed, the mean square error (MSE) rate of $g(\bx)$ is $O\big(\sigma^2 \vee \sigma^{2(1-\alpha)s}\big)$ as $\sigma\rightarrow 0$. By developing new methods to establish the minimax lower bounds under standard Gaussian shift model, we show that this rate is indeed minimax optimal and so is $g(\bx)$. The minimax rate implies a sharp threshold on the smoothness $s$ such that for only $f$ with smoothness above the threshold, $f(\btheta)$ can be estimated efficiently with an MSE rate of the order $O(\sigma^2)$. Normal approximation and asymptotic efficiency were proved for $g(\bx)$ under mild restrictions. Furthermore, we propose a data-driven procedure to develop an adaptive estimator when the covariance matrix $\bSigma$ is unknown. Numerical simulations are presented to validate our analysis. The simplicity of implementation and its superiority over the plug-in approach indicate the new estimator can be applied to a broad range of real world applications.

Deep neural networks (DNNs) have been expanded into medical fields and triggered the revolution of some medical applications by extracting complex features and achieving high accuracy and performance, etc. On the contrast, the large-scale network brings high requirements of both memory storage and computation resource, especially for portable medical devices and other embedded systems. In this work, we first train a DNN for pneumonia detection using the dataset provided by RSNA Pneumonia Detection Challenge [4]. To overcome hardware limitation for implementing large-scale networks, we develop a systematic structured weight pruning method with filter sparsity, column sparsity and combined sparsity. Experiments show that we can achieve up to 36x compression ratio compared to the original model with 106 layers, while maintaining no accuracy degradation. We evaluate the proposed methods on an embedded low-power device, Jetson TX2, and achieve low power usage and high energy efficiency. Keywords: Pneumonia detection · YOLO · structured weight pruning.

Abstract-- We develop algorithms with low regret for learning episodic Markov decision processes based on kernel approximation techniques. The algorithms are based on both the Upper Confidence Bound (UCB) as well as Posterior or Thompson Sampling (PSRL) philosophies, and work in the general setting of continuous state and action spaces when the true unknown transition dynamics are assumed to have smoothness induced by an appropriate Reproducing Kernel Hilbert Space (RKHS). I. INTRODUCTION The goal of reinforcement learning (RL) is to learn optimal behavior by repeated interaction with an unknown environment, usually modeled as a Markov Decision Process (MDP). Performance is typically measured by the amount of interaction, in terms of episodes or rounds, needed to arriv e at an optimal (or near-optimal) policy; this is also known as the sample complexity of RL [1]. The sample complexity objective encourages efficient exploration across states a nd actions, but, at the same time, is indifferent to the reward earned during the learning phase.

Despite their tremendous success in a wide range of applications, deep neural network (DNN) models are inherently vulnerable to two types of malicious manipulations: adversarial inputs, which are crafted samples that deceive target DNNs, and backdoored models, which are forged DNNs that misbehave on trigger-embedded inputs. While prior work has intensively studied the two attack vectors in parallel, there is still a lack of understanding about their fundamental connection, which is critical for assessing the holistic vulnerability of DNNs deployed in realistic settings. In this paper, we bridge this gap by conducting the first systematic study of the two attack vectors within a unified framework. More specifically, (i) we develop a new attack model that integrates both adversarial inputs and backdoored models; (ii) with both analytical and empirical evidence, we reveal that there exists an intricate "mutual reinforcement" effect between the two attack vectors; (iii) we demonstrate that this effect enables a large spectrum for the adversary to optimize the attack strategies, such as maximizing attack evasiveness with respect to various defenses and designing trigger patterns satisfying multiple desiderata; (v) finally, we discuss potential countermeasures against this unified attack and their technical challenges, which lead to several promising research directions.

Modern machine learning models are often so complex that they achieve vanishing classification error on the training set. Max-margin linear classifiers are among the simplest classification methods that have zero training error (with linearly separable data). Despite this simplicity, their high-dimensional behavior is not yet completely understood. We assume to be given i.i.d. data $(y_i,{\boldsymbol x}_i)$, $i\le n$ with ${\boldsymbol x}_i\sim {\sf N}({\boldsymbol 0},{\boldsymbol \Sigma})$ a $p$-dimensional Gaussian feature vector, and $y_i \in\{+1,-1\}$ a label whose distribution depends on a linear combination of the covariates $\langle {\boldsymbol \theta}_*,{\boldsymbol x}_i\rangle$. We consider the proportional asymptotics $n,p\to\infty$ with $p/n\to \psi$, and derive exact expressions for the limiting prediction error. Our asymptotic results match simulations already when $n,p$ are of the order of a few hundreds. We explore several choices for the the pair $({\boldsymbol \theta}_*,{\boldsymbol \Sigma})$, and show that the resulting generalization curve (test error error as a function of the overparametrization ratio $\psi=p/n$) is qualitatively different, depending on this choice. In particular we consider a specific structure of $({\boldsymbol \theta}_*,{\boldsymbol \Sigma})$ that captures the behavior of nonlinear random feature models or, equivalently, two-layers neural networks with random first layer weights. In this case, we observe that the test error is monotone decreasing in the number of parameters. This finding agrees with the recently developed `double descent' phenomenology for overparametrized models.

In this paper we propose a novel observer-based method to improve the safety and security of connected and automated vehicle (CAV) transportation. The proposed method combines model-based signal filtering and anomaly detection methods. Specifically, we use adaptive extended Kalman filter (AEKF) to smooth sensor readings of a CAV based on a nonlinear car-following model. Using the car-following model the subject vehicle (i.e., the following vehicle) utilizes the leading vehicle's information to detect sensor anomalies by employing previously-trained One Class Support Vector Machine (OCSVM) models. This approach allows the AEKF to estimate the state of a vehicle not only based on the vehicle's location and speed, but also by taking into account the state of the surrounding traffic. A communication time delay factor is considered in the car-following model to make it more suitable for real-world applications. Our experiments show that compared with the AEKF with a traditional $\chi^2$-detector, our proposed method achieves a better anomaly detection performance. We also demonstrate that a larger time delay factor has a negative impact on the overall detection performance.

In variational inference, the complicated target is approximated by a closest member relative to the Kullback-Leibler (KL) divergence in a pre-specified family of tractable densities. In many large-scale machine learning applications including clustering problems [11, 32], image classification [25, 27] and topic models [21, 7], variational inference can be orders of magnitude faster than the traditional sampling based approaches such as Markov Chain Monte Carlo (MCMC). In particular, by turning the integration, or sampling, problem into an optimization problem, variational inference can take advantage of modern optimization tools such as stochastic optimization techniques [20, 17] and distributed optimization architecture [1, 8] for further improving its efficiency. Among various approximating schemes, mean-field approximation is the most common type of variational inference that is conceptually simple, implementation-wise easy and particularly suitable for problems involving large numbers of latent variables. The word "mean-field" is originated from the mean-field theory in physics where despite complex interactions among many particles in a many (infinite) body system, all interactions to any one particle can be approximated by a single averaged effect from a "mean-field". In variational inference, by restricting the approximating family of the mean-field to be all density functions that are fully factorized over (blocks of) unknown variables, the associated optimization problem of finding a closest weih2@illinois.edu

Racial and ethnic disparities in access to healthcare in the United States is well-known and documented [1]. Health disparities are defined to be differences in health ou tcomes and causes among different groups of people. Health equity is achieved when everyone has the same opportunity to be as healthy as possible. We have a very good handle on the types of health disparities i n the US healthcare system, but the causes for these disparities are complex [2, 3] - such as inco me, education, socioeconomic conditions, neighborhood and community influence, public policy, and so cietal structure. Achieving health equity also necessitates a complex set of programs and interventions, a nd several public and private initiatives have tried to address this problem over the past decades.

We present the first estimation of the mass and spin of Kerr black holes resulting from the coalescence of binary black holes using a deep neural network. The network is trained on the full publicly available catalog of numerical simulations of gravitational waves emission by binary black hole systems. The network prediction for non-precessing binaries as well as precessing binaries is compared with existing fits in the LIGO-Virgo software package when existing. For the non-precessing case, the absolute error distribution has a root mean square error of $2.6 \cdot 10^{-3}$ for the final mass (twice lower than the existing fits) and $3 \cdot 10^{-3}$ for the final spin (similarly to the existing fits). We also estimate of the final mass in the precessing case, where we obtain a RMSE of $1 \cdot 10^{-3}$ of the absolute error distribution. It is $8 \cdot 10^{-3}$ when predicting the spin of the black hole resulting from a precessing binary, against $1.1 \cdot 10^{-2}$ for the existing fits.