On the Classification of Dynamical Data Streams Using Novel “Anti–Bayesian” Techniques

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Adaptive estimation and change detection of correlation and quantiles for evolving data streams

Streaming data processing is increasingly playing a central role in enterprise data architectures due to an abundance of available measurement data from a wide variety of sources and advances in data capture and infrastructure technology. Data streams arrive, with high frequency, as never-ending sequences of events, where the underlying data generating process always has the potential to evolve. Business operations often demand real-time processing of data streams for keeping models up-to-date and timely decision-making. For example in cybersecurity contexts, analysing streams of network data can aid the detection of potentially malicious behaviour. Many tools for statistical inference cannot meet the challenging demands of streaming data, where the computational cost of updates to models must be constant to ensure continuous processing as data scales. Moreover, these tools are often not capable of adapting to changes, or drift, in the data. Thus, new tools for modelling data streams with efficient data processing and model updating capabilities, referred to as streaming analytics, are required. Regular intervention for control parameter configuration is prohibitive to the truly continuous processing constraints of streaming data. There is a notable absence of such tools designed with both temporal-adaptivity to accommodate drift and the autonomy to not rely on control parameter tuning. Streaming analytics with these properties can be developed using an Adaptive Forgetting (AF) framework, with roots in adaptive filtering. The fundamental contributions of this thesis are to extend the streaming toolkit by using the AF framework to develop autonomous and temporally-adaptive streaming analytics. The first contribution uses the AF framework to demonstrate the development of a model, and validation procedure, for estimating time-varying parameters of bivariate data streams from cyber-physical systems. This is accompanied by a novel continuous monitoring change detection system that compares adaptive and non-adaptive estimates. The second contribution is the development of a streaming analytic for the correlation coefficient and an associated change detector to monitor changes to correlation structures across streams. This is demonstrated on cybersecurity network data. The third contribution is a procedure for estimating time-varying binomial data with thorough exploration of the nuanced behaviour of this estimator. The final contribution is a framework to enhance extant streaming quantile estimators with autonomous, temporally-adaptive properties. In addition, a novel streaming quantile procedure is developed and demonstrated, in an extensive simulation study, to show appealing performance.Open Acces

Information-Geometric Optimization Algorithms: A Unifying Picture via Invariance Principles

We present a canonical way to turn any smooth parametric family of probability distributions on an arbitrary search space $X$ into a continuous-time black-box optimization method on $X$, the \emph{information-geometric optimization} (IGO) method. Invariance as a design principle minimizes the number of arbitrary choices. The resulting \emph{IGO flow} conducts the natural gradient ascent of an adaptive, time-dependent, quantile-based transformation of the objective function. It makes no assumptions on the objective function to be optimized. The IGO method produces explicit IGO algorithms through time discretization. It naturally recovers versions of known algorithms and offers a systematic way to derive new ones. The cross-entropy method is recovered in a particular case, and can be extended into a smoothed, parametrization-independent maximum likelihood update (IGO-ML). For Gaussian distributions on $\mathbb{R}^d$, IGO is related to natural evolution strategies (NES) and recovers a version of the CMA-ES algorithm. For Bernoulli distributions on $\{0,1\}^d$, we recover the PBIL algorithm. From restricted Boltzmann machines, we obtain a novel algorithm for optimization on $\{0,1\}^d$. All these algorithms are unified under a single information-geometric optimization framework. Thanks to its intrinsic formulation, the IGO method achieves invariance under reparametrization of the search space $X$, under a change of parameters of the probability distributions, and under increasing transformations of the objective function. Theory strongly suggests that IGO algorithms have minimal loss in diversity during optimization, provided the initial diversity is high. First experiments using restricted Boltzmann machines confirm this insight. Thus IGO seems to provide, from information theory, an elegant way to spontaneously explore several valleys of a fitness landscape in a single run.Comment: Final published versio

Revisiting the Economics of Privacy: Population Statistics and Confidentiality Protection as Public Goods

This paper has been replaced with http://digitalcommons.ilr.cornell.edu/ldi/37. We consider the problem of the public release of statistical information about a population–explicitly accounting for the public-good properties of both data accuracy and privacy loss. We first consider the implications of adding the public-good component to recently published models of private data publication under differential privacy guarantees using a Vickery-Clark-Groves mechanism and a Lindahl mechanism. We show that data quality will be inefficiently under-supplied. Next, we develop a standard social planner’s problem using the technology set implied by (ε, δ)-differential privacy with (α, β)-accuracy for the Private Multiplicative Weights query release mechanism to study the properties of optimal provision of data accuracy and privacy loss when both are public goods. Using the production possibilities frontier implied by this technology, explicitly parameterized interdependent preferences, and the social welfare function, we display properties of the solution to the social planner’s problem. Our results directly quantify the optimal choice of data accuracy and privacy loss as functions of the technology and preference parameters. Some of these properties can be quantified using population statistics on marginal preferences and correlations between income, data accuracy preferences, and privacy loss preferences that are available from survey data. Our results show that government data custodians should publish more accurate statistics with weaker privacy guarantees than would occur with purely private data publishing. Our statistical results using the General Social Survey and the Cornell National Social Survey indicate that the welfare losses from under-providing data accuracy while over-providing privacy protection can be substantial

Differentially Private Fractional Frequency Moments Estimation with Polylogarithmic Space

We prove that Fp sketch, a well-celebrated streaming algorithm for frequency moments estimation, is differentially private as is when p ∈ (0, 1]. Fp sketch uses only polylogarithmic space, exponentially better than existing DP baselines and only worse than the optimal non-private baseline by a logarithmic factor. The evaluation shows that Fp sketch can achieve reasonable accuracy with differential privacy guarantee. The evaluation code is included in the supplementary material