Can We Learn to Beat the Best Stock

A novel algorithm for actively trading stocks is presented. While traditional expert advice and "universal" algorithms (as well as standard technical trading heuristics) attempt to predict winners or trends, our approach relies on predictable statistical relations between all pairs of stocks in the market. Our empirical results on historical markets provide strong evidence that this type of technical trading can "beat the market" and moreover, can beat the best stock in the market. In doing so we utilize a new idea for smoothing critical parameters in the context of expert learning

Generalization Bounds: Perspectives from Information Theory and PAC-Bayes

A fundamental question in theoretical machine learning is generalization. Over the past decades, the PAC-Bayesian approach has been established as a flexible framework to address the generalization capabilities of machine learning algorithms, and design new ones. Recently, it has garnered increased interest due to its potential applicability for a variety of learning algorithms, including deep neural networks. In parallel, an information-theoretic view of generalization has developed, wherein the relation between generalization and various information measures has been established. This framework is intimately connected to the PAC-Bayesian approach, and a number of results have been independently discovered in both strands. In this monograph, we highlight this strong connection and present a unified treatment of generalization. We present techniques and results that the two perspectives have in common, and discuss the approaches and interpretations that differ. In particular, we demonstrate how many proofs in the area share a modular structure, through which the underlying ideas can be intuited. We pay special attention to the conditional mutual information (CMI) framework; analytical studies of the information complexity of learning algorithms; and the application of the proposed methods to deep learning. This monograph is intended to provide a comprehensive introduction to information-theoretic generalization bounds and their connection to PAC-Bayes, serving as a foundation from which the most recent developments are accessible. It is aimed broadly towards researchers with an interest in generalization and theoretical machine learning.Comment: 222 page

New Statistical Learning Methods for Evaluating Dynamic Treatment Regimes and Optimal Dosing

Dynamic treatment regimes (DTRs) have gained increasing interest in the field of personalized health care in the last two decades, as they provide a sequence of individualized decision rules for treating patients over time. In a DTR, treatment is adapted in response to the changes in an individual's disease progression and health care history. However, specific challenges emerge when applying the current methods of DTR in practice. For example, a treatment decision often happens after a medical test, and is thus nested within the decision of whether a test is needed or not. Such nested test-and-treat strategies are attractive to improve cost-effectiveness. In the first project of this dissertation, we develop a Step-adjusted Tree-based Learning (SAT-Learning) method to estimate the optimal DTR within such a step-nested multiple-stage multiple-treatment dynamic decision framework using test-and-treat observational data. At each step within each stage, we combine a doubly robust semiparametric estimator via Augmented Inverse Probability Weighting with a tree-based reinforcement learning procedure to achieve the counterfactual optimization. SAT-Learning is robust and easy to interpret for the strategies of disease screening and subsequent treatments when necessary. We applied our method to a Johns Hopkins University prostate cancer active surveillance dataset to evaluate the necessity of prostate biopsy and identify the optimal test-and-treatment regimes for prostate cancer patients. Our second project is motivated by scenarios in medical practice where one need to decide on patients radiation or drug doses over time. Due to the complexity of continuous dose scales, few existing studies have extended their methods of multi-treatment decision making to a method to estimate the optimal DTR with continuous doses. We develop a new method, Kernel-Involved-Dosage-Decision learning (KIDD-Learning), which combines a kernel estimation of the dose-response function with a tree-based dose-search algorithm, in a multiple-stage setting. At each stage, KIDD-Learning recursively estimates a personalized dose-response function using kernel regression and then identifies the interpretable optimal dosage regime by growing an interpretable decision tree. The application of KIDD-Learning is illustrated by evaluating the dynamic dosage regimes of the adaptive radiation therapy using a Michigan Medicine liver cancer dataset. In KIDD-Learning, our algorithm splits each node of a tree-based decision rule from the root node to terminal nodes. This heuristic algorithm may fail to identify the optimal decision rule when there are critical tailoring variables hidden from an imperceptible parent node. Therefore, in the third project, we propose an important modification of KIDD-Learning, Stochastic Spline-Involved Tree Search (SSITS), to estimate a more robust optimal dosage regime. This new method uses a simulated annealing algorithm to stochastically search the space of tree-based decision rules. In each visited decision rule, a non-parametric smooth coefficient model is applied to estimate the dose-response function. We further implement backward induction to estimate the optimal regime from the final stage in a reverse sequential order to previous treatment stages. We apply SSITS to determine the optimal dosing strategy for patients treated with Warfarin using data from the International Warfarin Pharmacogenetics Consortium.PHDBiostatisticsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/163090/1/mingtang_1.pd

Detection of Lying Electrical Vehicles in Charging Coordination Application Using Deep Learning

The simultaneous charging of many electric vehicles (EVs) stresses the distribution system and may cause grid instability in severe cases. The best way to avoid this problem is by charging coordination. The idea is that the EVs should report data (such as state-of-charge (SoC) of the battery) to run a mechanism to prioritize the charging requests and select the EVs that should charge during this time slot and defer other requests to future time slots. However, EVs may lie and send false data to receive high charging priority illegally. In this paper, we first study this attack to evaluate the gains of the lying EVs and how their behavior impacts the honest EVs and the performance of charging coordination mechanism. Our evaluations indicate that lying EVs have a greater chance to get charged comparing to honest EVs and they degrade the performance of the charging coordination mechanism. Then, an anomaly based detector that is using deep neural networks (DNN) is devised to identify the lying EVs. To do that, we first create an honest dataset for charging coordination application using real driving traces and information revealed by EV manufacturers, and then we also propose a number of attacks to create malicious data. We trained and evaluated two models, which are the multi-layer perceptron (MLP) and the gated recurrent unit (GRU) using this dataset and the GRU detector gives better results. Our evaluations indicate that our detector can detect lying EVs with high accuracy and low false positive rate

Distributed implementations of the particle filter with performance bounds

The focus of the thesis is on developing distributed estimation algorithms for systems with nonlinear dynamics. Of particular interest are the agent or sensor networks (AN/SN) consisting of a large number of local processing and observation agents/nodes, which can communicate and cooperate with each other to perform a predefined task. Examples of such AN/SNs are distributed camera networks, acoustic sensor networks, networks of unmanned aerial vehicles, social networks, and robotic networks. Signal processing in the AN/SNs is traditionally centralized and developed for systems with linear dynamics. In the centralized architecture, the participating nodes communicate their observations (either directly or indirectly via a multi-hop relay) to a central processing unit, referred to as the fusion centre, which is responsible for performing the predefined task. For centralized systems with linear dynamics, the Kalman filter provides the optimal approach but suffers from several drawbacks, e.g., it is generally unscalable and also susceptible to failure in case the fusion centre breaks down. In general, no analytic solution can be determined for systems with nonlinear dynamics. Consequently, the conventional Kalman filter cannot be used and one has to rely on numerical approaches. In such cases, the sequential Monte Carlo approaches, also known as the particle filters, are widely used as approximates to the Bayesian estimators but mostly in the centralized configuration. Recently there has been a growing interest in distributed signal processing algorithms where: (i) There is no fusion centre; (ii) The local nodes do not have (require) global knowledge of the network topology, and; (iii) Each node exchanges data only within its local neighborhood. Distributed estimation have been widely explored for estimation/tracking problems in linear systems. Distributed particle filter implementations for nonlinear systems are still in their infancy and are the focus of this thesis. In the first part of this thesis, four different consensus-based distributed particle filter implementations are proposed. First, a constrained sufficient statistic based distributed implementation of the particle filter (CSS/DPF) is proposed for bearing-only tracking (BOT) and joint bearing/range tracking problems encountered in a number of applications including radar target tracking and robot localization. Although the number of parallel consensus runs in the CSS/DPF is lower compared to the existing distributed implementations of the particle filter, the CSS/DPF still requires a large number of iterations for the consensus runs to converge. To further reduce the consensus overhead, the CSS/DPF is extended to distributed implementation of the unscented particle filter, referred to as the CSS/DUPF, which require a limited number of consensus iterations. Both CSS/DPF and CSS/DUPF are specific to BOT and joint bearing/range tracking problems. Next, the unscented, consensus-based, distributed implementation of the particle filter (UCD /DPF) is proposed which is generalizable to systems with any dynamics. In terms of contributions, the UCD /DPF makes two important improvements to the existing distributed particle filter framework: (i) Unlike existing distributed implementations of the particle filter, the UCD /DPF uses all available global observations including the most recent ones in deriving the proposal distribution based on the distributed UKF, and; (ii) Computation of the global estimates from local estimates during the consensus step is based on an optimal fusion rule. Finally, a multi-rate consensus/fusion based framework for distributed implementation of the particle filter, referred to as the CF /DPF, is proposed. Separate fusion filters are designed to consistently assimilate the local filtering distributions into the global posterior by compensating for the common past information between neighbouring nodes. The CF /DPF offers two distinct advantages over its counterparts. First, the CF /DPF framework is suitable for scenarios where network connectivity is intermittent and consensus can not be reached between two consecutive observations. Second, the CF /DPF is not limited to the Gaussian approximation for the global posterior density. Numerical simulations verify the near-optimal performance of the proposed distributed particle filter implementations. The second half of the thesis focuses on the distributed computation of the posterior Cramer-Rao lower bounds (PCRLB). The current PCRLB approaches assume a centralized or hierarchical architecture. The exact expression for distributed computation of the PCRLB is not yet available and only an approximate expression has recently been derived. Motivated by the distributed adaptive resource management problems with the objective of dynamically activating a time-variant subset of observation nodes to optimize the network's performance, the thesis derives the exact expression, referred to as the dPCRLB, for computing the PCRLB for any AN/SN configured in a distributed fashion. The dPCRLB computational algorithms are derived for both the off-line conventional (non-conditional) PCRLB determined primarily from the state model, observation model, and prior knowledge of the initial state of the system, and the online conditional PCRLB expressed as a function of past history of the observations. Compared to the non-conditional dPCRLB, its conditional counterpart provides a more accurate representation of the estimator's performance and, consequently, a better criteria for sensor selection. The thesis then extends the dPCRLB algorithms to quantized observations. Particle filter realizations are used to compute these bounds numerically and quantify their performance for data fusion problems through Monte-Carlo simulations

High Lundquist Number Simulations of Parker\u27s Model of Coronal Heating: Scaling and Current Sheet Statistics Using Heterogeneous Computing Architectures

Parker\u27s model [Parker, Astrophys. J., 174, 499 (1972)] is one of the most discussed mechanisms for coronal heating and has generated much debate. We have recently obtained new scaling results for a 2D version of this problem suggesting that the heating rate becomes independent of resistivity in a statistical steady state [Ng and Bhattacharjee, Astrophys. J., 675, 899 (2008)]. Our numerical work has now been extended to 3D using high resolution MHD numerical simulations. Random photospheric footpoint motion is applied for a time much longer than the correlation time of the motion to obtain converged average coronal heating rates. Simulations are done for different values of the Lundquist number to determine scaling. In the high-Lundquist number limit (S \u3e 1000), the coronal heating rate obtained is consistent with a trend that is independent of the Lundquist number, as predicted by previous analysis and 2D simulations. We will present scaling analysis showing that when the dissipation time is comparable or larger than the correlation time of the random footpoint motion, the heating rate tends to become independent of Lundquist number, and that the magnetic energy production is also reduced significantly. We also present a comprehensive reprogramming of our simulation code to run on NVidia graphics processing units using the Compute Unified Device Architecture (CUDA) and report code performance on several large scale heterogenous machines

The MSSM Electroweak Phase Transition on the Lattice

We study the MSSM finite temperature electroweak phase transition with lattice Monte Carlo simulations, for a large Higgs mass (m_H ~ 95 GeV) and light stop masses (m_tR ~ 150...160 GeV). We employ a 3d effective field theory approach, where the degrees of freedom appearing in the action are the SU(2) and SU(3) gauge fields, the weakly interacting Higgs doublet, and the strongly interacting stop triplet. We determine the phase diagram, the critical temperatures, the scalar field expectation values, the latent heat, the interface tension and the correlation lengths at the phase transition points. Extrapolating the results to the infinite volume and continuum limits, we find that the transition is stronger than indicated by 2-loop perturbation theory, guaranteeing that the MSSM phase transition is strong enough for baryogenesis in this regime. We also study the possibility of a two-stage phase transition, in which the stop field gets an expectation value in an intermediate phase. We find that a two-stage transition exists non-perturbatively, as well, but for somewhat smaller stop masses than in perturbation theory. Finally, the latter stage of the two-stage transition is found to be extremely strong, and thus it might not be allowed in the cosmological environment.Comment: 43 pages, 17 figure

Randomized Dynamical Decoupling Strategies and Improved One-Way Key Rates for Quantum Cryptography

The present thesis deals with various methods of quantum error correction. It is divided into two parts. In the first part, dynamical decoupling methods are considered which have the task of suppressing the influence of residual imperfections in a quantum memory. The suppression is achieved by altering the dynamics of an imperfect quantum memory with the help of a sequence of local unitary operations applied to the qudits. Whereas up to now the operations of such decoupling sequences have been constructed in a deterministic fashion, strategies are developed in this thesis which construct the operations by random selection from a suitable set. Furthermore, it is investigated if and how the discussed decoupling strategies can be employed to protect a quantum computation running on the quantum memory. The second part of the thesis deals with quantum error-correcting codes and protocols for quantum key distribution. The focus is on the BB84 and the 6-state protocol making use of only one-way communication during the error correction and privacy amplification steps. It is shown that by adding additional errors to the preliminary key (a process called noisy preprocessing) followed by the use of a structured block code, higher secure key rates may be obtained. For the BB84 protocol it is shown that iterating the combined preprocessing leads to an even higher gain.Comment: PhD thesis, 223 pages, TU Darmstadt; http://tuprints.ulb.tu-darmstadt.de/1389

On the Distribution of Orbital Poles of Milky Way Satellites

In numerous studies of the outer Galactic halo some evidence for accretion has been found. If the outer halo did form in part or wholly through merger events, we might expect to find coherent streams of stars and globular clusters following similar orbits as their parent objects, which are assumed to be present or former Milky Way dwarf satellite galaxies. We present a study of this phenomenon by assessing the likelihood of potential descendant ``dynamical families'' in the outer halo. We conduct two analyses: one that involves a statistical analysis of the spatial distribution of all known Galactic dwarf satellite galaxies (DSGs) and globular clusters, and a second, more specific analysis of those globular clusters and DSGs for which full phase space dynamical data exist. In both cases our methodology is appropriate only to members of descendant dynamical families that retain nearly aligned orbital poles today. Since the Sagittarius dwarf (Sgr) is considered a paradigm for the type of merger/tidal interaction event for which we are searching, we also undertake a case study of the Sgr system and identify several globular clusters that may be members of its extended dynamical family. (ABRIDGED)Comment: accepted by ApJ, 57 pages, 13 figures, AASTeX forma