Recent exploration of optimal individualized decision rules (IDRs) for patients in precision medicine has attracted a lot of attention due to the heterogeneous responses of patients to different treatments. In the existing literature of precision medicine, an optimal IDR is defined as a decision function mapping from the patients' covariate space into the treatment space that maximizes the expected outcome of each individual. Motivated by the concept of Optimized Certainty Equivalent (OCE) introduced originally in \cite{ben1986expected} that includes the popular conditional-value-of risk (CVaR) \cite{rockafellar2000optimization}, we propose a decision-rule based optimized covariates dependent equivalent (CDE) for individualized decision making problems. Our proposed IDR-CDE broadens the existing expected-mean outcome framework in precision medicine and enriches the previous concept of the OCE. Numerical experiments demonstrate that our overall approach outperforms existing methods in estimating optimal IDRs under heavy-tail distributions of the data.

We prove that the norm version of the adaptive stochastic gradient method (AdaGrad-Norm) achieves a linear convergence rate for a subset of either strongly convex functions or non-convex functions that satisfy the Polyak-Lojasiewicz (PL) inequality. The paper introduces the notion of Restricted Uniform Inequality of Gradients (RUIG), which describes the uniform lower bound for the norm of the stochastic gradients with respect to the distance to the optimal solution. RUIG plays the key role in proving the robustness of AdaGrad-Norm to its hyper-parameter tuning. On top of RUIG, we develop a novel two-stage framework to prove linear convergence of AdaGrad-Norm without knowing the parameters of the objective functions: Stage I: the step-size decrease fast such that it reaches to Stage II; Stage II: the step-size decreases slowly and converges. This framework can likely be extended to other adaptive stepsize algorithms. The numerical experiments show desirable agreement with our theories.

Similarity plays a fundamental role in many areas, including data mining, machine learning, statistics and various applied domains. Inspired by the success of ensemble methods and the flexibility of trees, we propose to learn a similarity kernel called rpf-kernel through random projection forests (rpForests). Our theoretical analysis reveals a highly desirable property of rpf-kernel: far-away (dissimilar) points have a low similarity value while nearby (similar) points would have a high similarity}, and the similarities have a native interpretation as the probability of points remaining in the same leaf nodes during the growth of rpForests. The learned rpf-kernel leads to an effective clustering algorithm--rpfCluster. On a wide variety of real and benchmark datasets, rpfCluster compares favorably to K-means clustering, spectral clustering and a state-of-the-art clustering ensemble algorithm--Cluster Forests. Our approach is simple to implement and readily adapt to the geometry of the underlying data. Given its desirable theoretical property and competitive empirical performance when applied to clustering, we expect rpf-kernel to be applicable to many problems of an unsupervised nature or as a regularizer in some supervised or weakly supervised settings.

Recently, a special type of data poisoning (DP) attack targeting Deep Neural Network (DNN) classifiers, known as a backdoor, was proposed. These attacks do not seek to degrade classification accuracy, but rather to have the classifier learn to classify to a target class whenever the backdoor pattern is present in a test example. Launching backdoor attacks does not require knowledge of the classifier or its training process - it only needs the ability to poison the training set with (a sufficient number of) exemplars containing a sufficiently strong backdoor pattern (labeled with the target class). Here we address post-training detection of backdoor attacks in DNN image classifiers, seldom considered in existing works, wherein the defender does not have access to the poisoned training set, but only to the trained classifier itself, as well as to clean examples from the classification domain. This is an important scenario because a trained classifier may be the basis of e.g. a phone app that will be shared with many users. Detecting backdoors post-training may thus reveal a widespread attack. We propose a purely unsupervised anomaly detection (AD) defense against imperceptible backdoor attacks that: i) detects whether the trained DNN has been backdoor-attacked; ii) infers the source and target classes involved in a detected attack; iii) we even demonstrate it is possible to accurately estimate the backdoor pattern. We test our AD approach, in comparison with alternative defenses, for several backdoor patterns, data sets, and attack settings and demonstrate its favorability. Our defense essentially requires setting a single hyperparameter (the detection threshold), which can e.g. be chosen to fix the system's false positive rate.

The architecture of Transformer is based entirely on self-attention, and has been shown to outperform models that employ recurrence on sequence transduction tasks such as machine translation. The superior performance of Transformer has been attributed to propagating signals over shorter distances, between positions in the input and the output, compared to the recurrent architectures. We establish connections between the dynamics in Transformer and recurrent networks to argue that several factors including gradient flow along an ensemble of multiple weakly dependent paths play a paramount role in the success of Transformer. We then leverage the dynamics to introduce {\em Multiresolution Transformer Networks} as the first architecture that exploits hierarchical structure in data via self-attention. Our models significantly outperform state-of-the-art recurrent and hierarchical recurrent models on two real-world datasets for query suggestion, namely, \aol and \amazon. In particular, on AOL data, our model registers at least 20\% improvement on each precision score, and over 25\% improvement on the BLEU score with respect to the best performing recurrent model. We thus provide strong evidence that recurrence is not essential for modeling hierarchical structure.

In this paper we introduce Feature Gradients, a gradient-based search algorithm for feature selection. Our approach extends a recent result on the estimation of learnability in the sublinear data regime by showing that the calculation can be performed iteratively (i.e., in mini-batches) and in linear time and space with respect to both the number of features D and the sample size N . This, along with a discrete-to-continuous relaxation of the search domain, allows for an efficient, gradient-based search algorithm among feature subsets for very large datasets. Crucially, our algorithm is capable of finding higher-order correlations between features and targets for both the N > D and N < D regimes, as opposed to approaches that do not consider such interactions and/or only consider one regime. We provide experimental demonstration of the algorithm in small and large sample-and feature-size settings.

A novel active learning-based Gaussian process metamodelling strategy for estimating the full probability distribution in forward UQ analysis Ziqi Wang a, Marco Broccardo b a Earthquake Engineering Research and Test Center, Guangzhou University, China b Swiss Seismological Service, SED, ETH Z urich, SwitzerlandAbstract This paper proposes an active learning-based Gaussian process (AL-GP) metamodelling method to estimate the cumulative as well as complementary cumulative distribution function (CDF/CCDF) for forward uncertainty quantification (UQ) problems. Within the field of UQ, previous studies focused on developing AL-GP approaches for reliability (rare event probability) analysis of expensive black-box solvers. A naive iteration of these algorithms with respect to different CDF/CCDF threshold values would yield a discretized CDF/CCDF. However, this approach inevitably leads to a trade off between accuracy and computational efficiency since both depend (in opposite way) on the selected discretization. In this study, a specialized error measure and a learning function are developed such that the resulting AL-GP method is able to efficiently estimate the CDF/CCDF for a specified range of interest without an explicit dependency on discretization. Particularly, the proposed AL-GP method is able to simultaneously provide accurate CDF and CCDF estimation in their median-low probability regions. Three numerical examples are introduced to test and verify the proposed method. Introduction In a broad sense, uncertainty quantification (UQ) refers to the theory and practice to obtain quantitative understanding on the influences of uncertainties present within computational or real physical models. There are intrinsic connections between various branches of UQ, and attempts are made to develop unified UQ frameworks [4][5]. This study focuses on a central problem in forward UQ problems, the estimation of distribution function, i.e. cumulative and complementary cumulative distribution function (CDF/CCDF).

By: William Schoenberg (University of Bergen, Norway) Abstract This work re presents a new approach which generates then analyzes a highly non - linear complex system of differential equations to do interpretable time series forecasting at a high level of accuracy. This approach provides insight and understanding into the mechanisms responsible for gener ating past and future behavior. Core to this method is the construction of a highly non - linear complex system of differential equations that is then analyzed to determine the origins of behavior. This paper demonstrates the technique on Mass and Senge's two state Inventory Workforce model ( 1975) and then explores its application to the real world problem of organogenesis in mice . The organogenesis application consists of a fourteen - state system where the generated set of equations reproduces observed behavior with a high level of accuracy ( 0.88 0 Introduction: Accurate time series forecasting is very important to a variety of scientific fields, engineering disciplines, and socially constructed systems including businesses, and governments (Palit & Popovic, 2006) . Past effort s on this problem have focused on developing more accurate methods or models useful for predicting time series data, starting with linear statistical models and evolving into non - linear models and ultimately machine learning techniques (Bontempi, et, al, 2012) .

We investigate the efficiency of k-means in terms of both statistical and computational requirements. More precisely, we study a Nystr\"om approach to kernel k-means. We analyze the statistical properties of the proposed method and show that it achieves the same accuracy of exact kernel k-means with only a fraction of computations. Indeed, we prove under basic assumptions that sampling $\sqrt{n}$ Nystr\"om landmarks allows to greatly reduce computational costs without incurring in any loss of accuracy. To the best of our knowledge this is the first result of this kind for unsupervised learning.

In this work, we introduce a recently developed early classification mechanism to satellite-based agricultural monitoring. It augments existing classification models by an additional stopping probability based on the previously seen information. This mechanism is end-to-end trainable and derives its stopping decision solely from the observed satellite data. W e show results on field parcels in central Europe where sufficient ground truth data is available for an empiric evaluation of the results with local phenological information obtained from authorities. W e observe that the recurrent neural network outfitted with this early classification mechanism was able to distinguish the many of the crop types before the end of the vegetative period. Further, we associated these stopping times with evaluated ground truth information and saw that the times of classification were related to characteristic events of the observed plants' phenology.