An artificial immune system for continuous analysis of time-varying data

M. Neal, An Artificial Immune System for Continuous Analysis of Time-Varying Data, in Proceedings of the 1st International Conference on Artificial Immune Systems (ICARIS), 2002, eds J Timmis and P J Bentley, volume 1, pages 76-85,

Skin Color-Based Video Segmentation under Time-Varying Illumination

A novel approach for real-time skin segmentation in video sequences is described. The approach enables reliable skin segmentation despite wide variation in illumination during tracking. An explicit second order Markov model is used to predict evolution of the skin-color (HSV) histogram over time. Histograms are dynamically updated based on feedback from the current segmentation and predictions of the Markov model. The evolution of the skin-color distribution at each frame is parameterized by translation, scaling and rotation in color space. Consequent changes in geometric parameterization of the distribution are propagated by warping and resampling the histogram. The parameters of the discrete-time dynamic Markov model are estimated using Maximum Likelihood Estimation, and also evolve over time. The accuracy of the new dynamic skin color segmentation algorithm is compared to that obtained via a static color model. Segmentation accuracy is evaluated using labeled ground-truth video sequences taken from staged experiments and popular movies. An overall increase in segmentation accuracy of up to 24% is observed in 17 out of 21 test sequences. In all but one case the skin-color classification rates for our system were higher, with background classification rates comparable to those of the static segmentation.

Probabilistic Fréchet means for time varying persistence diagrams

© 2015, Institute of Mathematical Statistics. All rights reserved.In order to use persistence diagrams as a true statistical tool, it would be very useful to have a good notion of mean and variance for a set of diagrams. In [23], Mileyko and his collaborators made the first study of the properties of the Fréchet mean in (Dp, Wp), the space of persistence diagrams equipped with the p-th Wasserstein metric. In particular, they showed that the Fréchet mean of a finite set of diagrams always exists, but is not necessarily unique. The means of a continuously-varying set of diagrams do not themselves (necessarily) vary continuously, which presents obvious problems when trying to extend the Fréchet mean definition to the realm of time-varying persistence diagrams, better known as vineyards. We fix this problem by altering the original definition of Fréchet mean so that it now becomes a probability measure on the set of persistence diagrams; in a nutshell, the mean of a set of diagrams will be a weighted sum of atomic measures, where each atom is itself a persistence diagram determined using a perturbation of the input diagrams. This definition gives for each N a map (Dp)^N→ℙ(Dp). We show that this map is Hölder continuous on finite diagrams and thus can be used to build a useful statistic on vineyards.

Communication system model for information rate evaluation of differential detection over time-varying channels

A communication system model for mutual information performance analysis of multiple-symbol differential M-phase shift keying over time-correlated, time-varying flat-fading communication channels is developed. This model is a finite-state Markov (FSM) equivalent channel representing the cascade of the differential encoder, FSM channel model and differential decoder. A state-space approach is used to model channel phase time correlations. The equivalent model falls in a class that facilitates the use of the forward backward algorithm, enabling the important information theoretic results to be evaluated. Using such a model, one is able to calculate mutual information for differential detection over time-varying fading channels with an essentially finite time set of correlations, including the Clarke fading channel. Using the equivalent channel, it is proved and corroborated by simulations that multiple-symbol differential detection preserves the channel information capacity when the observation interval approaches infinity.

Mutual information performance of differential MPSK detection over time-varying channels

This paper provides mutual information performance analysis of multiple-symbol differential WSK (M-phase shift keying) over time-correlated, time-varying flat-fading communication channels. A state space approach is used to model time correlation of time varying channel phase. This approach captures the dynamics of time correlated, time-varying channels and enables exploitation of the forward-backward algorithm for mutual information performance analysis. It is shown that the differential decoding implicitly uses a sequence of innovations of the channel process time correlation and this sequence is essentially uncorrelated. It enables utilization of multiple-symbol differential detection, as a form of block-by-block maximum likelihood sequence detection for capacity achieving mutual information performance. It is shown that multiple-symbol differential ML detection of BPSK and QPSK practically achieves the channel information capacity with observation times only on the order of a few symbol intervals

On information rates of time-varying fading channels modeled as finite-state Markov channels

We study information rates of time-varying flat-fading channels (FFC) modeled as finite-state Markov channels (FSMC). FSMCs have two main applications for FFCs: modeling channel error bursts and decoding at the receiver. Our main finding in the first application is that receiver observation noise can more adversely affect higher-order FSMCs than lower-order FSMCs, resulting in lower capacities. This is despite the fact that the underlying higher-order FFC and its corresponding FSMC are more predictable. Numerical analysis shows that at low to medium SNR conditions (SNR lsim 12 dB) and at medium to fast normalized fading rates (0.01 lsim fDT lsim 0.10), FSMC information rates are non-increasing functions of memory order. We conclude that BERs obtained by low-order FSMC modeling can provide optimistic results. To explain the capacity behavior, we present a methodology that enables analytical comparison of FSMC capacities with different memory orders. We establish sufficient conditions that predict higher/lower capacity of a reduced-order FSMC, compared to its original high-order FSMC counterpart. Finally, we investigate the achievable information rates in FSMC-based receivers for FFCs. We observe that high-order FSMC modeling at the receiver side results in a negligible information rate increase for normalized fading rates fDT lsim 0.01.

Efficient Evaluation of Multidimensional Time-Varying Density Forecasts

We propose two simple evaluation methods for time varying density forecasts of continuous higher dimensional random variables. Both methods are based on the probability integral transformation for unidimensional forecasts. The first method tests multinormal densities and relies on the rotation of the coordinate system. The advantage of the second method is not only its applicability to any continuous distribution but also the evaluation of the forecast accuracy in specific regions of its domain as defined by the user’s interest. We show that the latter property is particularly useful for evaluating a multidimensional generalization of the Value at Risk. In simulations and in an empirical study, we examine the performance of both tests.

Modeling Multivariate Interest Rates Using Time-Varying Copulas and Reducible Nonlinear Stochastic Differential Equations

We propose a new approach for modeling nonlinear multivariate interest rate processes based on time-varying copulas and reducible stochastic differential equations (SDEs). In the modeling of the marginal processes, we consider a class of nonlinear SDEs that are reducible to Ornstein--Uhlenbeck (OU) process or Cox, Ingersoll, and Ross (1985) (CIR) process. The reducibility is achieved via a nonlinear transformation function. The main advantage of this approach is that these SDEs can account for nonlinear features, observed in short-term interest rate series, while at the same time leading to exact discretization and closed-form likelihood functions. Although a rich set of specifications may be entertained, our exposition focuses on a couple of nonlinear constant elasticity volatility (CEV) processes, denoted as OU-CEV and CIR-CEV, respectively. These two processes encompass a number of existing models that have closed-form likelihood functions. The transition density, the conditional distribution function, and the steady-state density function are derived in closed form as well as the conditional and unconditional moments for both processes. In order to obtain a more flexible functional form over time, we allow the transformation function to be time varying. Results from our study of U.S. and UK short-term interest rates suggest that the new models outperform existing parametric models with closed-form likelihood functions. We also find the time-varying effects in the transformation functions statistically significant. To examine the joint behavior of interest rate series, we propose flexible nonlinear multivariate models by joining univariate nonlinear processes via appropriate copulas. We study the conditional dependence structure of the two rates using Patton (2006a) time-varying symmetrized Joe--Clayton copula. We find evidence of asymmetric dependence between the two rates, and that the level of dependence is positively related to the level of the two rates. (JEL: C13, C32, G12) Copyright The Author 2010. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org, Oxford University Press.

Adaptive calibration of a three-microphone system for acoustic waveguide characterization under time-varying conditions

The pressure and velocity field in a one-dimensional acoustic waveguide can be sensed in a non-intrusive manner using spatially distributed microphones. Experimental characterization with sensor arrangements of this type has many applications in measurement and control. This paper presents a method for measuring the acoustic variables in a duct under fluctuating propagation conditions with specific focus on in-system calibration and tracking of the system parameters of a three-microphone measurement configuration. The tractability of the non-linear optimization problem that results from taking a parametric approach is investigated alongside the influence of extraneous measurement noise on the parameter estimates. The validity and accuracy of the method are experimentally assessed in terms of the ability of the calibrated system to separate the propagating waves under controlled conditions. The tracking performance is tested through measurements with a time-varying mean flow, including an experiment conducted under propagation conditions similar to those in a wind instrument during playing.

Reducible Diffusions with Time-Varying Transformations with Application to Short-Term Interest Rates

Reducible diffusions (RDs) are nonlinear transformations of analytically solvable Basic Diffusions (BDs). Hence, by construction RDs are analytically tractable and flexible diffusion processes. Existing literature on RDs has mostly focused on time-homogeneous transformations, which to a significant extent fail to explore the full potential of RDs from both theoretical and practical points of view. In this paper, we propose flexible and economically justifiable time variations to the transformations of RDs. Concentrating on the Constant Elasticity Variance (CEV) RDs, we consider nonlinear dynamics for our time-varying transformations with both deterministic and stochastic designs. Such time variations can greatly enhance the flexibility of RDs while maintaining sufficient tractability of the resulting models. In the meantime, our modeling approach enjoys the benefits of classical inferential techniques such as the Maximum Likelihood (ML). Our application to the UK and the US short-term interest rates suggests that from an empirical point of view time-varying transformations are highly relevant and statistically significant. We expect that the proposed models can describe more truthfully the dynamic time-varying behavior of economic and financial variables and potentially improve out-of-sample forecasts significantly.

Time-Varying Liquidity and Momentum Profits

A basic intuition is that arbitrage is easier when markets are most liquid. Surprisingly, we find that momentum profits are markedly larger in liquid market states. This finding is not explained by variation in liquidity risk, time-varying exposure to risk factors, or changes in macroeconomic condition, cross-sectional return dispersion, and investor sentiment. The predictive performance of aggregate market illiquidity for momentum profits uniformly exceed that of market return and market volatility states. While momentum strategies are unconditionally unprofitable in US, Japan, and Eurozone countries in the last decade, they are substantial following liquid market states.