Probabilistic Sense Research Articles

Sequential Randomized Algorithms for Robust Convex Optimization

Sequential randomized algorithms are considered for robust convex optimization which minimizes a linear objective function subject to a parameter dependent convex constraint. Employing convex optimization and random sampling of parameter, these algorithms enable us to obtain a suboptimal solution within reasonable computational time. The suboptimal solution is feasible in a probabilistic sense and the suboptimal value belongs to an interval which contains the optimal value. The maximum of the interval is the optimal value of the robust convex optimization plus a specified tolerance. On the other hand, its minimum is the optimal value of the chance constrained optimization which is a probabilistic relaxation of the robust convex optimization, with high probability.

A Time–Frequency Masking Based Random Finite Set Particle Filtering Method for Multiple Acoustic Source Detection and Tracking

Considering that multiple talkers may appear simultaneously, a time–frequency (TF) masking based random finite set (RFS) particle filtering (PF) method is developed for multiple acoustic source detection and tracking. The time-delay of arrival (TDOA) measurements of multiple sources are extracted by using a time–frequency masking technique, by which each source’s TF bins are clustered and separated in a joint gain-ratio and time-delay histogram. Since a joint detection and tracking problem is considered, both source positions and source numbers are time-varying and need to be estimated. The tracker is built within a RFS Bayesian filtering framework. Essentially, an RFS process is used to characterize the source dynamics that include source appearance/dissappearance and motion trajectories. Latent variables are also introduced to indicate source dynamics and measurement-source associations. Subsequently, a Rao–Blackwellization PF technique is employed so that the source position state can be marginalized and only the latent variables are estimated by using the PF. The main advantage of the proposed approach is that hypothesis-pruning is formulated in a full probabilistic sense. The performance of the proposed approach is demonstrated in real speech recordings as well as in simulated room environments.

On the global stability of an iterative scheme in a probabilistic Menger space

This paper studies the convergence properties of an iterative process which involves sequences of convergent self-mappings in probabilistic Menger spaces which are used to generate the sequences of interest. The convergent self-mappings under consideration satisfy conditions of either uniform or point-wise convergence, in a probabilistic sense, to a self-mapping on the same abstract space of the considered probabilistic metric space. Furthermore, the self-mappings of the considered sequence satisfy a probabilistic ϕ-contractive condition which is based on the use of a control ϕ-function. Some illustrative examples are also discussed.

Study of controlled dense coding with some discrete tripartite and quadripartite states

The paper presents a detailed study of controlled dense coding scheme for different types of three and four-particle states. It consists of GHZ state, GHZ type states, maximal slice (MS), state, 4-particle GHZ state and W class of states. It is shown that GHZ-type states can be used for controlled dense coding in a probabilistic sense. We have shown relations among parameter of GHZ type state, concurrence of the shared bipartite state by two parties with respect to GHZ type and Charlie's measurement angle θ. The GHZ states as a special case of MS states, depending on parameters, have also been considered here. We have seen that tripartite W state and quadripartite W state cannot be used in controlled dense coding whereas |Wn〉ABC states can be used probabilistically. Finally, we have investigated controlled dense coding scheme for tripartite qutrit states.

FS3: A sampling based method for top‐k frequent subgraph mining

Mining labeled subgraph is a popular research task in data mining because of its potential application in many different scientific domains. All the existing methods for this task explicitly or implicitly solve the subgraph isomorphism task, which is computationally expensive, and thus they suffer from the lack of scalability problem when the graphs in the input database are large. In this work, we propose FS3, which is a sampling‐based method. It mines a small collection of subgraphs that are most frequent in the probabilistic sense. FS3 performs a Markov chain Monte Carlo (MCMC) sampling over the space of a fixed‐size subgraphs such that the potentially frequent subgraphs are sampled more often. Besides, FS3 is equipped with an innovative queue manager. It stores the sampled subgraph in a finite queue over the course of mining in such a manner that the top‐k positions in the queue contain the most frequent subgraphs. Our experiments on the database of large graphs show that FS3 is efficient and obtains subgraphs that are the most frequent among the subgraphs of a given size.

Robust stabilisation of time-varying delay systems with probabilistic uncertainties

For robust stabilisation of time-varying delay systems, only sufficient conditions are available to date. A natural question is as follows: if the existing sufficient conditions are not satisfied, and hence no controllers can be found, what can one do to improve the stability performance of time-varying delay systems? This question is addressed in this paper when there is a probabilistic structure on the parameter uncertainty set. A randomised algorithm is proposed to design a state-feedback controller, which stabilises the system over the uncertainty domain in a probabilistic sense. The capability of the designed controller is quantified by the probability of stability of the resulting closed-loop system. The accuracy of the solution obtained from the randomised algorithm is also analysed. Finally, numerical examples are used to illustrate the effectiveness and advantages of the developed controller design approach.

Geodynamic inversion to constrain the non-linear rheology of the lithosphere

One of the main methods to determine the strength of the lithosphere is by estimating it's effective elastic thickness. This method assumes that the lithosphere is a thin elastic plate that floats on the mantle and uses both topography and gravity anomalies to estimate the plate thickness. Whereas this seems to work well for oceanic plates, it has given controversial results in continental collision zones. For most of these locations, additional geophysical data sets such as receiver functions and seismic tomography exist that constrain the geometry of the lithosphere and often show that it is rather complex. Yet, lithospheric geometry by itself is insufficient to understand the dynamics of the lithosphere as this also requires knowledge of the rheology of the lithosphere. Laboratory experiments suggest that rocks deform in a viscous manner if temperatures are high and stresses low, or in a plastic/brittle manner if the yield stress is exceeded. Yet, the experimental results show significant variability between various rock types and there are large uncertainties in extrapolating laboratory values to nature, which leaves room for speculation. An independent method is thus required to better understand the rheology and dynamics of the lithosphere in collision zones. The goal of this paper is to discuss such an approach. Our method relies on performing numerical thermomechanical forward models of the present-day lithosphere with an initial geometry that is constructed from geophysical data sets. We employ experimentally determined creep-laws for the various parts of the lithosphere, but assume that the parameters of these creep-laws as well as the temperature structure of the lithosphere are uncertain. This is used as a priori information to formulate a Bayesian inverse problem that employs topography, gravity, horizontal and vertical surface velocities to invert for the unknown material parameters and temperature structure. In order to test the general methodology, we first perform a geodynamic inversion of a synthetic forward model of intraoceanic subduction with known parameters. This requires solving an inverse problem with 14–16 parameters, depending on whether temperature is assumed to be known or not. With the help of a massively parallel direct-search combined with a Markov Chain Monte Carlo method, solving the inverse problem becomes feasible. Results show that the rheological parameters and particularly the effective viscosity structure of the lithosphere can be reconstructed in a probabilistic sense. This also holds, with somewhat larger uncertainties, for the case where the temperature distribution is parametrized. Finally, we apply the method to a cross-section of the India–Asia collision system. In this case, the number of parameters is larger, which requires solving around 1.9 × 106 forward models. The resulting models fit the data within their respective uncertainty bounds, and show that the Indian mantle lithosphere must have a high viscosity. Results for the Tibetan plateau are less clear, and both models with a weak Asian mantle lithosphere and with a weak Asian lower crust fit the data nearly equally well.

Newton’s method for first-order stochastic functional partial differential equations

We apply Newton’s method to hyperbolic stochastic functional partial differential equations of the first order driven by a multidimensional Brownian motion. We prove a first-order convergence and a second-order convergence in a probabilistic sense.

Improved model output statistics of numerical weather prediction based irradiance forecasts for solar power applications

The fast growth of solar photo-voltaic energy and the issues related to its integration in the power system are leading to an increased importance of forecasts of solar irradiance. Irradiance forecasts based on numerical weather prediction (NWP) models may be downscaled to finer spatial and temporal granularity and corrected for systematic biases by applying so-called model output statistics (MOS). This paper presents a MOS routine that is based on a large set of meteorological variables that are available from standard NWP output and a clear sky model. The method is based on a stepwise linear regression algorithm yielding a regression model with a set of variables that best explains the observed forecast error. The resulting irradiance forecasts for the first forecast day averaged over an ensemble of 27 stations corrected with this model reduces the relative root mean square error (rRMSE) to 22.7% compared to a rRMSE of 37.8% of uncorrected forecasts and a rRMSE of 25.6% of forecasts corrected with a method based on only the solar zenith angle and the predicted clear sky index – a method that is a current standard in NWP based irradiance forecasts. Furthermore, since this new method takes more meteorological information into account than the current standard method, the increase in skill evaluated in a probabilistic sense is even higher, because a forecast probability density is obtained that better reflects the sensitivity of forecast errors to atmospheric conditions.

Nature or nurture? Clues from the distribution of specific star formation rates in SDSS galaxies

This work investigates the main mechanism(s) that regulate the specific star formation rate (SSFR) in nearby galaxies, cross-correlating two proxies of this quantity -- the equivalent width of the \Ha\ line and the $(u-r)$ colour -- with other physical properties (mass, metallicity, environment, morphology, and the presence of close companions) in a sample of $\sim82500$ galaxies extracted from the Sloan Digital Sky Survey (SDSS). The existence of a relatively tight `ageing sequence' in the colour-equivalent width plane favours a scenario where the secular conversion of gas into stars (i.e. `nature') is the main physical driver of the instantaneous SSFR and the gradual transition from a `chemically primitive' (metal-poor and intensely star-forming) state to a `chemically evolved' (metal-rich and passively evolving) system. Nevertheless, environmental factors (i.e. `nurture') are also important. In the field, galaxies may be temporarily affected by discrete `quenching' and `rejuvenation' episodes, but such events show little statistical significance in a probabilistic sense, and we find no evidence that galaxy interactions are, on average, a dominant driver of star formation. Although visually classified mergers tend to display systematically higher EW(H$\alpha$) and bluer $(u-r)$ colours for a given luminosity, most galaxies with high SSFR have uncertain morphologies, which could be due to either internal or external processes. Field galaxies of early and late morphological types are consistent with the gradual `ageing' scenario, with no obvious signatures of a sudden decrease in their SSFR. In contrast, star formation is significantly reduced and sometimes completely quenched on a short time scale in dense environments, where many objects are found on a `quenched sequence' in the colour-equivalent width plane.

Control of Parallel Non-observable Queues: Asymptotic Equivalence and Optimality of Periodic Policies

We consider a queueing system composed of a dispatcher that routes jobs to a set of non-observable queues working in parallel. In this setting, the fundamental problem is which policy should the dispatcher implement to minimize the stationary mean waiting time of the incoming jobs. We present a structural property that holds in the classic scaling of the system where the network demand (arrival rate of jobs) grows proportionally with the number of queues. Assuming that each queue of type r is replicated k times, we consider a set of policies that are periodic with period [Formula: see text] and such that exactly pr jobs are sent in a period to each queue of type r. When k → ∞, our main result shows that all the policies in this set are equivalent, in the sense that they yield the same mean stationary waiting time, and optimal, in the sense that no other policy having the same aggregate arrival rate to all queues of a given type can do better in minimizing the stationary mean waiting time. This property holds in a strong probabilistic sense. Furthermore, the limiting mean waiting time achieved by our policies is a convex function of the arrival rate in each queue, which facilitates the development of a further optimization aimed at solving the fundamental problem above for large systems.

Asymptotic Normality of the Maximum Pseudolikelihood Estimator for Fully Visible Boltzmann Machines.

Boltzmann machines (BMs) are a class of binary neural networks for which there have been numerous proposed methods of estimation. Recently, it has been shown that in the fully visible case of the BM, the method of maximum pseudolikelihood estimation (MPLE) results in parameter estimates, which are consistent in the probabilistic sense. In this brief, we investigate the properties of MPLE for the fully visible BMs further, and prove that MPLE also yields an asymptotically normal parameter estimator. These results can be used to construct confidence intervals and to test statistical hypotheses. These constructions provide a closed-form alternative to the current methods that require Monte Carlo simulation or resampling. We support our theoretical results by showing that the estimator behaves as expected in simulation studies.

Oppose, Support, or Hedge? Distributional Effects, Regulatory Pressure, and Business Strategy in Environmental Politics

What explains the choice of corporate political strategy in environmental politics? Drawing on recent models of actor strategy formation in political economy, this article argues that basic material interests of firms are translated into strategies in the context of institutional environments. I advance a typological model that posits how distributional effects—positive versus negative—and perceived regulatory pressure—low versus high—interact in leading firms to adopt one of four ideal-type strategies: opposition, hedging, support, and non-participation. This article examines the model through the case of corporate strategies in the making of the European Union’s Emission Trading Scheme. The article contributes to theory-building on business strategy in environmental politics by offering a probabilistic explanatory model, and it flags hedging strategies as an increasingly prevalent form of business behavior.

Model the nonlinear instability of wall-bounded shear flows as a rare event: a study on two-dimensional Poiseuille flow

In this work, we study the nonlinear instability of two-dimensional (2D) wall-bounded shear flows from the large deviation point of view. The main idea is to consider the Navier–Stokes equations perturbed by small noise in force and then examine the noise-induced transitions between the two coexisting stable solutions due to the subcritical bifurcation. When the amplitude of the noise goes to zero, the Freidlin–Wentzell (F–W) theory of large deviations defines the most probable transition path in the phase space, which is the minimizer of the F–W action functional and characterizes the development of the nonlinear instability subject to small random perturbations. Based on such a transition path we can define a critical Reynolds number for the nonlinear instability in the probabilistic sense. Then the action-based stability theory is applied to study the 2D Poiseuille flow in a short channel.

Wellposedness for stochastic continuity equations with Ladyzhenskaya–Prodi–Serrin condition

We consider the stochastic divergence-free continuity equations with Ladyzhenskaya–Prodi–Serrin condition. Wellposedness is proved meanwhile uniqueness may fail for the deterministic PDE. The main issue of strong uniqueness, in the probabilistic sense, relies on stochastic characteristic method and the generalized Ito–Wentzell–Kunita formula. The stability property for the unique solution is proved with respect to the initial data. Moreover, a persistence result is established by a representation formula.

Probabilistic Analysis of Balancing Scores for Causal Inference

Propensity scores are often used for stratification of treatment and control groups of subjects in observational data to remove confounding bias when estimating of causal effect of the treatment on an outcome in so-called potential outcome causal modeling framework. In this article, we try to get some insights into basic behavior of the propensity scores in a probabilistic sense. We do a simple analysis of their usage confining to the case of discrete confounding covariates and outcomes. While making clear about behavior of the propensity score our analysis shows how the so-called prognostic score can be derived simultaneously. However the prognostic score is derived in a limited sense in the current literature whereas our derivation is more general and shows all possibilities of having the score. And we call it outcome score. We argue that application of both the propensity score and the outcome score is the most efficient way for reduction of dimension in the confounding covariates as opposed to current belief that the propensity score alone is the most efficient way.

Randomization and the Gross–Pitaevskii Hierarchy

We study the Gross–Pitaevskii hierarchy on the spatial domain $${\mathbb{T}^3}$$ . By using an appropriate randomization of the Fourier coefficients in the collision operator, we prove an averaged form of the main estimate which is used in order to contract the Duhamel terms that occur in the study of the hierarchy. In the averaged estimate, we do not need to integrate in the time variable. An averaged spacetime estimate for this range of regularity exponents then follows as a direct corollary. The range of regularity exponents that we obtain is $${\alpha > \frac{3}{4}}$$ . It was shown in our previous joint work with Gressman (J Funct Anal 266(7):4705–4764, 2014) that the range $${\alpha > 1}$$ is sharp in the corresponding deterministic spacetime estimate. This is in contrast to the non-periodic setting, which was studied by Klainerman and Machedon (Commun Math Phys 279(1):169–185, 2008), where the spacetime estimate is known to hold whenever $${\alpha \geq 1}$$ . The goal of our paper is to extend the range of α in this class of estimates in a probabilistic sense. We use the new estimate and the ideas from its proof in order to study randomized forms of the Gross–Pitaevskii hierarchy. More precisely, we consider hierarchies similar to the Gross–Pitaevskii hierarchy, but in which the collision operator has been randomized. For these hierarchies, we show convergence to zero in low regularity Sobolev spaces of Duhamel expansions of fixed deterministic density matrices. We believe that the study of the randomized collision operators could be the first step in the understanding of a nonlinear form of randomization.

A statistical framework with stiffness proportional damage sensitive features for structural health monitoring

A modal parameter based damage sensitive feature (DSF) is defined to mimic the relative change in any diagonal element of the stiffness matrix of a model of a structure. The damage assessment is performed in a statistical pattern recognition framework using empirical complementary cumulative distribution functions (ECCDFs) of the DSFs extracted from measured operational vibration response data. Methods are discussed to perform probabilistic structural health assessment with respect to the following questions: (a) "Is there a change in the current state of the structure compared to the baseline state?", (b) "Does the change indicate a localized stiffness reduction or increase?", with the latter representing a situation of retrofitting operations, and (c) "What is the severity of the change in a probabilistic sense?". To identify a range of normal structural variations due to environmental and operational conditions, lower and upper bound ECCDFs are used to define the baseline structural state. Such an approach attempts to decouple "non-damage" related variations from damage induced changes, and account for the unknown environmental/operational conditions of the current state. The damage assessment procedure is discussed using numerical simulations of ambient vibration testing of a bridge deck system, as well as shake table experimental data from a 4-story steel frame.

No-Reference Image Quality Assessment and Blind Deblurring with Sharpness Metrics Exploiting Fourier Phase Information

It has been known for more than 30 years that most of the geometric content of a digital image is encoded in the phase of its Fourier transform. This has led to several works that exploit the global (Fourier) or local (Wavelet) phase information of an image to achieve quality assessment, edge detection, and, more recently, blind deblurring. We here propose a deeper insight into three recent sharpness metrics (global phase coherence, sharpness index, and a simplified version of it), which all measure in a probabilistic sense the surprisingly small total variation of an image compared to that of certain associated random phase fields. We exhibit several theoretical connections between these indices and study their behavior on a general class of stationary random fields. We also use experiments to highlight the behavior of these metrics with respect to blur, noise, and deconvolution artifacts (ringing). Finally, we propose an application to isotropic blind deblurring and illustrate its efficiency on several examples.

Control of parallel non-observable queues: Asymptotic equivalence and optimality of periodic policies

We consider a queueing system composed of a dispatcher that routes deterministically jobs to a set of non-observable queues working in parallel. In this setting, the fundamental problem is which policy should the dispatcher implement to minimize the stationary mean waiting time of the incoming jobs. We present a structural property that holds in the classic scaling of the system where the network demand (arrival rate of jobs) grows proportionally with the number of queues. Assuming that each queue of type r is replicated k times, we consider a set of policies that are periodic with period k r pr and such that exactly pr jobs are sent in a period to each queue of type r. When k → ∞, our main result shows that all the policies in this set are equivalent, in the sense that they yield the same mean stationary waiting time, and optimal, in the sense that no other policy having the same aggregate arrival rate to all queues of a given type can do better in minimizing the stationary mean waiting time. This property holds in a strong probabilistic sense. Furthermore, the limiting mean waiting time achieved by our policies is a convex function of the arrival rate in each queue, which facilitates the development of a further optimization aimed at solving the fundamental problem above for large systems.