the em algorithm an old folk song sung to a fast new tune celebrating the 20th anniversary of the presentation of the paper by dempster laird and rubin which popularized the em algorithm we investigate after a brief historical account strategies that aim to make the em algorithm converge faster while maintaining its simplicity and stability e g automatic monotone convergence in likelihood first we introduce the idea of a working parameter to facilitate the search for efficient data augmentation schemes and thus fast em implementations second summarizing various recent extensions of the em algorithm we formulate a general alternating expectation conditional maximization algorithm aecm that couples flexible data augmentation schemes with model reduction schemes to achieve efficient computations we illustrate these methods using multivariate t models with known or unknown degrees of freedom and poisson models for image reconstruction we show through both empirical and theoretical evidence the potential for a dramatic reduction in computational time with little increase in human effort we also discuss the intrinsic connection between em type algorithms and the gibbs sampler and the possibility of using the techniques presented here to speed up the latter the main conclusion of the paper is that with the help of statistical considerations it is possible to construct algorithms that are simple stable and fast

simultaneous adaptive control and identification via the weighted least square algorithm in this note we prove the almost sure convergence of the proposed adaptive control and identification algorithms involving a weighted least square parameter estimator the analysis presented here strengthens the previous results achieved in this context the proposed algorithm and the analysis achieve the convergence of the tracking error in a strong sense at an asymptotically arithmetic rate the stronger result is obtained under a regularity and persistency condition introduced in this note which also ensures that with probability one the algorithm affords equal weighting to all the measurements after a finite number of iterations under these conditions it is also shown that the parameter estimation error also converges to zero in the context of siso armax models it is proved that the regularity and persistency conditions are satisfied under mild mixing conditions on the noise and no pole zero cancellation in the plant input output transfer function by a random perturbation of the reference trajectory

state estimation and detectability of probabilistic discrete event systems a probabilistic discrete event system pdes is a nondeterministic discrete event system where the probabilities of nondeterministic transitions are specified state estimation problems of pdes are more difficult than those of non probabilistic discrete event systems in our previous papers we investigated state estimation problems for non probabilistic discrete event systems we defined four types of detectabilities and derived necessary and sufficient conditions for checking these detectabilities in this paper we extend our study to state estimation problems for pdes by considering the probabilities the first step in our approach is to convert a given pdes into a nondeterministic discrete event system and find sufficient conditions for checking probabilistic detectabilities next to find necessary and sufficient conditions for checking probabilistic detectabilities we investigate the convergence of event sequences in pdes an event sequence is convergent if along this sequence it is more and more certain that the system is in a particular state we derive conditions for convergence and hence for detectabilities we focus on systems with complete event observation and no state observation for better presentation the theoretical development is illustrated by a simplified example of nephritis diagnosis

variance based extragradient methods with line search for stochastic variational inequalities in this paper we propose dynamic sampled stochastic approximated ds sa extragradient methods for stochastic variational inequalities svis that are robust with respect to an unknown lipschitz c

convergence in mean for els based adaptive control abstract almost sure global convergence results are available for stochastic adaptive control this note looks at the nontrivial technical details required to ensure corresponding convergence in p th mean results both convergence results are strong but are not implied by the other and so together almost sure and p th mean convergence are stronger than either the other aim of this paper is to show that the combination of these two forms of convergence results makes the stability results more robust and potentially of more practical significance

lms algorithms for tracking slow markov chains with applications to hidden markov estimation and adaptive multiuser detection this paper analyzes the tracking properties of the least mean squares lms algorithm when the underlying parameter evolves according to a finite state markov chain with infrequent jumps first using perturbed liapunov function methods mean square error estimates are obtained for the tracking error then using recent results on two time scale markov chains mean ordinary differential equation and diffusion approximation results are obtained it is shown that a sequence of the centered tracking errors converges to an ordinary differential equation moreover a suitably scaled sequence of the tracking errors converges weakly to a diffusion process it is also shown that iterate averaging of the tracking algorithm results in optimal asymptotic convergence rate in an appropriate sense two application examples analysis of the performance of an adaptive multiuser detection algorithm in a direct sequence code division multiple access ds cdma system and tracking analysis of the state of a hidden markov model hmm with infrequent jumps are presented

a one measurement form of simultaneous perturbation stochastic approximation the simultaneous perturbation stochastic approximation spsa algorithm has proven very effective for difficult multivariate optimization problems where it is not possible to obtain direct gradient information as discussed to date spsa is based on a highly efficient gradient approximation requiring only two measurements of the loss function independent of the number of parameters being estimated this note presents a form of spsa that requires only one function measurement for any dimension theory is presented that identifies the class of problems for which this one measurement form will be asymptotically superior to the standard two measurement form

ordinal criteria in stochastic multicriteria acceptability analysis smaa abstract we suggest a method for providing descriptive information about the acceptability of decision alternatives in discrete co operative group decision making problems the new smaa o method is a variant of the stochastic multicriteria acceptability analysis smaa smaa o is designed for problems where criteria information for some or all criteria is ordinal that is experts or decision makers have ranked the alternatives according to each ordinal criterion considerable savings can be obtained if rank information for some or all the criteria is sufficient for making decisions without significant loss of quality the approach is particularly useful for group decision making when the group can agree on the use of an additive decision model but only partial preference information or none at all is available

on the design of a stable adaptive filter for state estimation in high dimensional systems design of specific parametrized gain structures provides a new tool for ensuring stability of reduced order filter for high dimensional systems which is optimized adaptively in the minimum prediction error framework

adaptive control with recursive identification for stochastic linear systems this paper presents a stochastic adaptive control algorithm which is shown to possess the following properties when applied to a possibly unstable inverse stable linear stochastic system with unknown parameters whenever that system satisfies a certain positive real condition on its moving average noise dynamics 1 the adaptive control part of the algorithm stabilizes and asymptotically optimizes the behavior of the system in the sense that the limit of the sample mean square variation of the output around a given demand level equals that of a minimum variance control strategy implemented with known parameters this optimal behavior is subject to an offset 2where 2is the variance of a dither signal added to the control action in order to produce a continually disturbed control for mu 2 0 it is shown that the input output process satisfies a persistent excitation property and hence subject to a simple identifiability condition the next property holds 2 the observed input and output of the controlled system may be taken as inputs to an approximate maximum likelihood algorithm aml which generates strongly consistent estimates of the system s parameters results are presented for the scalar and multivariable cases

classifying efficient alternatives in smaa using cross confidence factors abstract stochastic multicriteria acceptability analysis smaa is a family of methods for aiding multicriteria group decision making these methods are based on exploring the weight space in order to describe the preferences that make each alternative the most preferred one the main results of the analysis are rank acceptability indices central weight vectors and confidence factors for different alternatives the rank acceptability indices describe the variety of different preferences resulting in a certain rank for an alternative the central weight vectors represent the typical preferences favouring each alternative and the confidence factors measure whether the criteria data are sufficiently accurate for making an informed decision in some cases when the problem involves a large number of efficient alternatives the analysis may fail to discriminate between them this situation is revealed by low confidence factors in this paper we develop cross confidence factors which are based on computing confidence factors for alternatives using each other s central weight vectors the cross confidence factors can be used for classifying efficient alternatives into sets of similar and competing alternatives these sets are related to the concept of reference sets in data envelopment analysis dea but generalized for stochastic models forming these sets is useful when trying to identify one or more most preferred alternatives or suitable compromise alternatives the reference sets can also be used for evaluating whether criteria need to be measured more accurately and at which alternatives the measurements should be focused this may cause considerable savings in measurement costs we demonstrate the use of the cross confidence factors and reference sets using a real life example

asymptotically optimum recursive prediction error methods in adaptive estimation and control abstract the challenge taken up in this paper is to devise a parameter identification algorithm for linear discrete time stochastic plants which exploits the strengths of both the extended least squares els and the recursive prediction error rpe parameter estimation methods the focus is on adaptive control of parameterized state space models which exploit a priori plant information in that the unknown parameter vector r is of lower dimension than that for a corresponding input output model parameterized by a triple parameter estimation scheme consisting of els rpe and a hybrid of the two denoted hpe is proposed the purpose of the hpe scheme is to permit information flow from the els to rpe algorithms so as to effectively project rpe into a stability domain and to have it avoid local prediction error index minima that are not the global minimum

optimal bayesian experimental design for priors of compact support with application to shock tube experiments for combustion kinetics summary the analysis of reactive systems in combustion science and technology relies on detailed models comprising many chemical reactions that describe the conversion of fuel and oxidizer into products and the formation of pollutants shock tube experiments are a convenient setting for measuring the rate parameters of individual reactions the temperature pressure and concentration of reactants are chosen to maximize the sensitivity of the measured quantities to the rate parameter of the target reaction in this study we optimize the experimental setup computationally by optimal experimental design in a bayesian framework we approximate the posterior probability density functions pdf using truncated gaussian distributions in order to account for the bounded domain of the uniform prior pdf of the parameters the underlying gaussian distribution is obtained in the spirit of the laplace method more precisely the mode is chosen as the maximum a posteriori map estimate and the covariance is chosen as the negative inverse of the hessian of the misfit function at the map estimate the model related entities are obtained from a polynomial surrogate the optimality quantified by the information gain measures can be estimated efficiently by a rejection sampling algorithm against the underlying gaussian probability distribution rather than against the true posterior this approach offers a significant error reduction when the magnitude of the invariants of the posterior covariance are comparable with the size of the bounded domain of the prior we demonstrate the accuracy and superior computational efficiency of our method for shock tube experiments aiming to measure the model parameters of a key reaction which is part of the complex kinetic network describing the hydrocarbon oxidation in the experiments the initial temperature and fuel concentration are optimized with respect to the expected information gain in the estimation of the parameters of the target reaction rate we show that the expected information gain surface can change its shape dramatically according to the level of noise introduced into the synthetic data the information that can be extracted from the data saturates as a logarithmic function of the number of experiments and few experiments are needed when they are conducted at the optimal experimental design conditions furthermore inversion of the legacy data indicates the validity and robustness of our designs copyright 2016 john wiley sons ltd

stochastic approximation method with gradient averaging for unconstrained problems a stochastic approximation algorithm is studied in which random gradient estimates are averaged by an auxiliary filter convergence of the algorithm is proved under a rather general noise condition a practical version of the method is described and numerical results are given

robust estimation without positive real condition the strictly positive real spr condition on the noise model is necessary for a discrete time linear stochastic control system with unmodeled dynamics even so for a time invariant armax system in the past robust analysis of parameter estimation however this condition is hardly satisfied for a high order and or multidimensional system with correlated noise the main work in this paper is to show that for robust parameter estimation and adaptive tracking as well as closed loop system stabilization the spr condition is replaced by a stable matrix polynomial the main method is to design a two step recursive least squares algorithm with or without a weighted factor and with a fixed lag regressive vector and to define an adaptive control with bounded external excitation and with randomly varying truncation

multistep stochastic mirror descent for risk averse convex stochastic programs based on extended polyhedral risk measures we consider risk averse convex stochastic programs expressed in terms of extended polyhedral risk measures we derive computable confidence intervals on the optimal value of such stochastic programs using the robust stochastic approximation and the stochastic mirror descent smd algorithms when the objective functions are uniformly convex we also propose a multistep extension of the stochastic mirror descent algorithm and obtain confidence intervals on both the optimal values and optimal solutions numerical simulations show that our confidence intervals are much less conservative and are quicker to compute than previously obtained confidence intervals for smd and that the multistep stochastic mirror descent algorithm can obtain a good approximate solution much quicker than its nonmultistep counterpart

analysis and optimization of diagonally layered lattice schemes for mimo fading channels embodiments of the diagonal bell laboratories layered space time d blast architecture for multiple input multiple output mimo communication are developed wherein information symbol vectors are encoded using codewords from a lattice code called a diagonally layered lattice dll code which are formatted onto the diagonals of a space time frame decoding is done using a sphere decoder for each diagonal based on soft statistics obtained after zero forcing zf or minimum mean square error mmse filtering and decision feedback these operations give rise to an effective parallel channel model with channel gains with nonidentical statistics and additive noise which is gaussian in the zf filtering case and non gaussian in the mmse filtering case the so called full modulation diversity fmd property is nevertheless shown to yield the maximum achievable diversity orders over the mimo channel for both the zf and the mmse filtering based decoders respectively for any arbitrary fading distribution in the case of the independent identically distributed i i d rayleigh fading mimo channel with k transmit and n receive antennas with ngesk these diversity orders are nk k k 1 2 and nk for zf and mmse filtering based decoding respectively the error probability analysis also yields a design criterion for optimizing transmit power allocations several lattice design methods are proposed for the effective parallel channel models two methods are proposed to achieve high coding gain in the rayleigh fading mimo channel a third method is proposed that minimizes the exact symbol error probability sep and can be tailored for any given fading distribution a novel soft decision feedback decoder is also proposed based on the list sphere decoder to mitigate error propagation due to hard decision feedback the salient feature of the proposed dll schemes is that they have nearly full rate and full or high diversity order and yet a much lower decoding complexity than other existing full rate full diversity space time block codes stbcs the frame error probability fep performance of the optimized dll schemes for moderate to high spectral efficiencies and a wide range of signal to noise ratios snrs can be quite close to the performance of the best performing but more complex to decode stbcs moreover the proposed dll schemes significantly outperform other existing mimo systems of comparable decoding complexity

stochastic multicriteria acceptability analysis using the data envelopment model abstract data envelopment analysis dea and stochastic multicriteria acceptability analysis smaa 2 are methods for evaluating alternatives based on multiple criteria while dea is mainly an ex post tool used for classifying alternatives into efficient and inefficient ones smaa 2 is an ex ante tool for supporting multiple criteria decision making both methods use a kind of value function where the importance of criteria is modeled using weights unlike many other methods neither dea nor smaa 2 requires decision makers weights as input instead these so called non parametric methods explore the weight space in order to identify weights favorable for each alternative this paper introduces the smaa d method which is a combination of dea and smaa 2 smaa d can be characterized as an extension of dea to handle uncertain or imprecise data to provide stochastic efficiency measures alternatively the combined method can be seen as a variant of smaa 2 with a dea type value function

self convergence of weighted least squares with applications to stochastic adaptive control a recursive least squares algorithm with slowly decreasing weights for linear stochastic systems is found to have self convergence property i e it converges to a certain random vector almost surely irrespective of the control law design such algorithms enjoy almost the same nice asymptotic properties as the standard least squares this universal convergence result combined with a method of random regularization then easily can be applied to construct a self convergent and uniformly controllable estimated model and thus may enable us to form a general framework for adaptive control of possibly nonminimum phase autoregressive moving average with exogenous input armax systems as an application we give a simple solution to the well known stochastic adaptive pole placement and linear quadratic gaussian lqg control problems in the paper

technical communique on adaptive minimum variance regulation for non minimum phase plants adaptive minimum variance control is applied to nonminimum phase plants augmented with adaptive compensators the objective of the compensators is to achieve asymptotically a minimum phase property for the augmented plant with this property the minimum variance controller gives a stabilizing control signal the scheme proposed has interpretations as an adaptive quadratic index minimizing procedure and also as an adaptive pole assignment algorithm the advantage over other adaptive quadratic index minimizing procedures is simply that the weightings are made adaptive so as to guarantee convergence one feature not shared by other adaptive pole assignment schemes is that they conveniently specialize to simple minimum variance schemes when for these control energy constraints are not violated this paper presents only the discrete time adaptive regulator version companion papers give a full global convergence theory and pre processing augmentations for the stochastic tracking scheme versions

multivariate gaussian criteria in smaa abstract we consider stochastic multicriteria decision making problems with multiple decision makers in such problems the uncertainty or inaccuracy of the criteria measurements and the partial or missing preference information can be represented through probability distributions in many real life problems the uncertainties of criteria measurements may be dependent however it is often difficult to quantify these dependencies also most of the existing methods are unable to handle such dependency information in this paper we develop a method for handling dependent uncertainties in stochastic multicriteria group decision making problems we measure the criteria their uncertainties and dependencies using a stochastic simulation model the model is based on decision variables and stochastic parameters with given distributions based on the simulation results we determine for the criteria measurements a joint probability distribution that quantifies the uncertainties and their dependencies we then use the smaa 2 stochastic multicriteria acceptability analysis method for comparing the alternatives based on the criteria distributions we demonstrate the use of the method in the context of a strategic decision support model for a retailer operating in the liberated european electricity market

brief paper stochastic adaptive control using a modified least squares algorithm recent papers on stochastic adaptive control have established global convergence for algorithms using a stochastic approximation iteration however to date global convergence has not been established for algorithms incorporating a least squares iteration this paper establishes global convergence for a slightly modified least squares stochastic adaptive control algorithm it is shown that with probability one the algorithm will ensure that the system inputs and outputs are sample mean square bounded and the mean square output tracking error achieves its global minimum possible value for linear feedback control

ascent based monte carlo expectation maximization summary the expectation maximization em algorithm is a popular tool for maximizing likelihood functions in the presence of missing data unfortunately em often requires the evaluation of analytically intractable and high dimensional integrals the monte carlo em mcem algorithm is the natural extension of em that employs monte carlo methods to estimate the relevant integrals typically a very large monte carlo sample size is required to estimate these integrals within an acceptable tolerance when the algorithm is near convergence even if this sample size were known at the onset of implementation of mcem its use throughout all iterations is wasteful especially when accurate starting values are not available we propose a data driven strategy for controlling monte carlo resources in mcem the algorithm proposed improves on similar existing methods by recovering em s ascent i e likelihood increasing property with high probability being more robust to the effect of user defined inputs and handling classical monte carlo and markov chain monte carlo methods within a common framework because of the first of these properties we refer to the algorithm as ascent based mcem we apply ascent based mcem to a variety of examples including one where it is used to accelerate the convergence of deterministic em dramatically

least mean square algorithms with markov regime switching limit we analyze the tracking performance of the least mean square lms algorithm for adaptively estimating a time varying parameter that evolves according to a finite state markov chain we assume the markov chain jumps infrequently between the finite states at the same rate of change as the lms algorithm we derive mean square estimation error bounds for the tracking error of the lms algorithm using perturbed lyapunov function methods then combining results in two time scale markov chains with weak convergence methods for stochastic approximation we derive the limit dynamics satisfied by continuous time interpolation of the estimates unlike most previous analyzes of stochastic approximation algorithms the limit we obtain is a system of ordinary differential equations with regime switching controlled by a continuous time markov chain next to analyze the rate of convergence we take a continuous time interpolation of a scaled sequence of the error sequence and derive its diffusion limit somewhat remarkably for correlated regression vectors we obtain a jump markov diffusion finally two novel examples of the analysis are given for state estimation of hidden markov models hmms and adaptive interference suppression in wireless code division multiple access cdma networks

convergence rates of continuous time stochastic els parameter estimation discrete time convergence rates for extended least squares els algorithms are generalized to the continuous time case an essential difference in the estimation is the appropriate prefiltering while in the theory the existence of solutions of the stochastic equations is a concern

simulated annealing searching for an optimal temperature schedule a sizable part of the theoretical literature on simulated annealing deals with a property called convergence which asserts that the simulated annealing chain is in the set of global minimum states of the objective function with probability tending to 1 however in practice the convergent algorithms are considered too slow whereas a number of nonconvergent ones are usually preferred we attempt a detailed analysis of various temperature schedules examples will be given of when it is both practically and theoretically justified to use boiling fixed temperature or even fast cooling schedules which have a small probability of reaching global minima applications to traveling salesman problems of various sizes are also given

implementing stochastic multicriteria acceptability analysis abstract stochastic multicriteria acceptability analysis smaa is a family of methods for aiding multicriteria group decision making in problems with inaccurate uncertain or missing information these methods are based on exploring the weight space in order to describe the preferences that make each alternative the most preferred one or that would give a certain rank for a specific alternative the main results of the analysis are rank acceptability indices central weight vectors and confidence factors for different alternatives the rank acceptability indices describe the variety of different preferences resulting in a certain rank for an alternative the central weight vectors represent the typical preferences favouring each alternative and the confidence factors measure whether the criteria measurements are sufficiently accurate for making an informed decision the computations in smaa require the evaluation of multidimensional integrals that must in practice be computed numerically in this paper we present efficient methods for performing the computations through monte carlo simulation analyze the complexity and assess the accuracy of the presented algorithms we also test the efficiency of these methods empirically based on the tests the implementation is fast enough to analyze typical sized discrete problems interactively within seconds due to almost linear time complexity the method is also suitable for analysing very large decision problems for example discrete approximations of continuous decision problems

threshold accepting a general purpose optimization algorithm appearing superior to simulated annealing abstract a new general purpose algorithm for the solution of combinatorial optimization problems is presented the new threshold accepting method is even simpler structured than the wellknown simulated annealing approach the power of the new algorithm is demonstrated by computational results concerning the traveling salesman problem and the problem of the construction of error correcting codes moreover deterministic versions of the new heuristic turn out to perform nearly equally well consuming only a fraction of the computing time of the stochastic versions as an example the deterministic threshold accepting method yields very near to optimum tours for the famous 442 cities traveling salesman problem of grotschel within 1 to 2 s of cpu time

on line estimation of dynamic shock error models based on the kullback leibler information measure develops two sequential or on line estimation schemes in the time domain for dynamic shock error models which are special cases of errors in variables models the author s approach utilizes a state space representation of the model kalman filtering techniques and on line algorithms the first on line algorithm is based on the expectation maximization algorithm and uses a recursive gauss newton scheme to maximize the kullback leibler information measure the second on line algorithm the author proposes is a gradient based scheme and uses stochastic approximations to maximize the log likelihood in comparison to the off line maximum likelihood estimation scheme used in ghosh 1989 the author s on line algorithms have significantly reduced computational costs and negligible memory requirements simulations illustrate the satisfactory performance of the algorithms in estimating errors in variables systems with parameters that vary slowly with time or undergo infrequent jump changes

on sampling rates in simulation based recursions we consider the context of simulation based recursions that is recursions that involve quantities needing to be estimated using a stochastic simulation examples include stochastic adaptations of fixed point and gradient descent recursions obtained by replacing function and derivative values appearing within the recursion by their monte carlo counterparts the primary motivating settings are simulation optimization and stochastic root finding problems where the low point and the zero of a function are sought respectively with only monte carlo estimates of the functions appearing within the problem we ask how much monte carlo sampling needs to be performed within simulation based recursions in order that the resulting iterates remain consistent and more importantly efficient where efficient implies convergence at the fastest possible rate answering these questions involves trading off two types of error inherent in the iterates the deterministic error due to recursion and the stochastic er

convergence and logarithm laws of self tuning regulators abstract this paper starts with a survey of some recent results on least squares ls and ls based self tuning regulators str several long standing problems concerning the basic properties of ls based str such as stability optimality consistency and the best convergence rate are solved within a unified framework some previously related results are also subsumed and extended various new techniques for analysing ls based adaptive tracking systems are presented which may also be useful for analysing other adaptive control problems

ordinal data in multicriteria decision making a stochastic dominance approach to siting nuclear power plants abstract this paper addresses decision problems with ordinal data weights criterion scores a random sampling approach is proposed to generate quantitative values which are consistent with the underlying ordinal information an attractive feature of the approach is that it is applicable with mixed quantitative ordinal data another feature is that the approach can be extended to rankings with degrees of difference the outcome of the approach is a distribution of performance scores stochastic dominance concepts are proposed to arrive at a final ranking of alternatives an application of these procedures is given for a location study of nuclear power plants

optimization by simulated annealing an experimental evaluation part ii graph coloring and number partitioning this is the second in a series of three papers that empirically examine the competitiveness of simulated annealing in certain well studied domains of combinatorial optimization simulated annealing is a randomized technique proposed by s kirkpatrick c d gelatt and m p vecchi for improving local optimization algorithms here we report on experiments at adapting simulated annealing to graph coloring and number partitioning two problems for which local optimization had not previously been thought suitable for graph coloring we report on three simulated annealing schemes all of which can dominate traditional techniques for certain types of graphs at least when large amounts of computing time are available for number partitioning simulated annealing is not competitive with the differencing algorithm of n karmarkar and r m karp except on relatively small instances moreover if running time is taken into account natural annealing schemes cannot even outperform multiple random runs of the local optimization algorithms on which they are based in sharp contrast to the observed performance of annealing on other problems

stochastic approximation with averaging and feedback rapidly convergent on line algorithms consider the stochastic approximation x sub n 1 x sub n a sub n g x sub n spl xi sub n where 0 0 the averaging method is essentially off line in the sense that the actual sa iterate x sub n is not influenced by the averaging in many applications x sub n itself is of greatest interest since that is the operating parameter this paper deals with the problem of stochastic approximation with averaging and with appropriate feedback of the averages into the original algorithm it is shown both mathematically and via simulation that it works very well and has numerous advantages it is a clear improvement over the system x sub n by itself it is fairly robust and quite often it is much preferable to the use of the above averages without feedback the authors deal in particular with linear algorithms of the type appearing in parameter estimators adaptive noise cancellers channel equalizers adaptive control and similar applications the main development is for the constant parameter case because of its importance in applications but analogous results hold for the case where a sub n spl rarr 0

new optimization heuristics in a former paper we introduced a very effective new general purpose optimization principle we compared this method which we called threshold accepting ta with the well known simulated annealing sa method for discrete optimization the empirical results demonstrated the superiority of the ta algorithm in further experiments with the ta principle we discovered two new powerful optimization heuristics the great deluge algorithm gda and the record to record travel rrt these algorithms resemble in their structure the formerly studied ta and the sa method the differences lie in their acceptance rules for worse intermediate solutions both the gda and the rrt are essentially one parameter algorithms i e for the achievement of best possible performance a good choice is necessary only for a single parameter this is in contrast for instance to the classical as algorithm where it is necessary to choose carefully a certain sequence of parameters the so called annealing schedule the quality of the computational results obtained so far by rrt and gda shows that the new algorithms behave equally well as ta and thus a fortiori better than sa

smaa 2 stochastic multicriteria acceptability analysis for group decision making stochastic multicriteria acceptability analysis smaa is a multicriteria decision support method for multiple decision makers in discrete problems in smaa the decision makers need not express their preferences explicitly or implicitly instead the method is based on exploring the weight space in order to describe the valuations that would make each alternative the preferred one inaccurate or uncertain criteria values are represented by probability distributions from which the method computes confidence factors describing the reliability of the analysis in this paper we introduce the smaa 2 method which extends the original smaa by considering all ranks in the analysis in situations where the elitistic smaa may assess large acceptability only for extreme alternatives without sufficient majority support the more holistic smaa 2 analysis can be used to identify good compromise candidates the results are presented graphically we consider also situations where partial preference information is available we demonstrate the new method using a real life decision problem

central tendency minimum variance adaptive control the authors propose designing indirect adaptive controllers using measures of central tendency of the a posteriori probability function of the control for parameters that is given a knowledge of plant uncertainty at each time instant from estimation algorithms and a controller design rule controller parameters are sought which maximize the likelihood of achieving the control objectives the particular case of adaptive minimum variance control is studied in detail

decision aid for discrete multiple criteria decision making problems with imprecise data abstract we describe ways of aiding decision making with a discrete set of alternatives in many decision situations it is not possible to obtain explicit preference information from the decision makers instead useful decision aid can be provided to the decision makers by describing what kind of weighting of the criteria result in certain choices of the alternatives the suggested treatment is based on the basic ideas of the electre iii method the modelling of the preferences by pseudo criteria is especially helpful in case the data that is the criterion values are imprecise unlike electre iii no ranking of the alternatives is produced based on a minimum procedure in the exploitation of the outranking relations we provide information about the weights of the criteria that make a certain alternative the best we also present an interactive searching procedure in the weighting space the auxiliary optimization problems to be solved are nondifferentiable cases with both single and multiple decision makers are considered

convergence of adaptive minimum variance algorithms via weighting coefficient selection weighted least squares and related stochastic approximation algorithms are studied for parameter estimation adaptive state estimation adaptive n step ahead prediction and adaptive control in both white and colored noise environments for the fundamental algorithm which is the basis for the various applications the step size in the stochastic approximation versions and the weighting coefficient in the weighted least squares schemes are selected according to a readily calculated stability measure associated with the estimator the selection is guided by the convergence theory in this way strong global convergence of the parameter estimates state estimates and prediction or tracking errors is not only guaranteed under the appropriate noise passivity and stability or minimum phase conditions but the convergence is also as fast as it appears reasonable to achieve given the simplicity of the adaptive scheme

relative entropy rate based multiple hidden markov model approximation this paper proposes a novel relative entropy rate rer based approach for multiple hmm mhmm approximation of a class of discrete time uncertain processes under different uncertainty assumptions the model design problem is posed either as a min max optimisation problem or stochastic minimization problem on the rer between joint laws describing the state and output processes rather than the more usual rer between output processes a suitable filter is proposed for which performance results are established which bound conditional mean estimation performance and show that estimation performance improves as the rer is reduced these filter consistency and convergence bounds are the first results characterizing multiple hmm approximation performance and suggest that joint rer concepts provide a useful model selection criteria the proposed model design process and mhmm filter are demonstrated on an important image processing dim target detection problem

on the convergence of the self tuning algorithms based on nonmodified least squares self tuning servo control based on a nonmodified least squares algorithm is considered the fundamental result of the analysis is that the passivity of the two time varying operators depending on the noise process dynamics regression vector and the ponderation matrix sequence of the algorithm is essential for the global stability of the self tuning regulator the methodology can be applied to problems of adaptive prediction based on a nonmodified least squares algorithm and system parameter identification by a least squares algorithm with a priori prediction

persistence of excitation in extended least squares in least squares parameter estimation schemes persistency of excitation conditions on the plant states are required for consistent estimation in the case of extended least squares the persistency conditions are on the state estimates here these persistency of excitation conditions are translated into sufficiently rich conditions on the plant noise and inputs in the case of adaptive minimum variance control schemes the sufficiently rich conditions are on the noise and specified output trajectory with sufficiently rich input signals guaranteed convergence rates of prediction errors improve and it is conjectured that the algorithms are consequently more robust

a parallel decomposition method for nonconvex stochastic multi agent optimization problems this paper considers the problem of minimizing the expected value of a possibly nonconvex cost function parameterized by a random vector variable when the expectation cannot be computed accurately e g because the statistics of the random variables are unknown and or the computational complexity is prohibitive classical stochastic gradient methods for solving this problem may suffer from slow convergence in this paper we propose a stochastic parallel successive convex approximation based best response algorithm for general nonconvex stochastic sum utility optimization problems which arise naturally in the design of multi agent networks the proposed novel decomposition approach enables all users to update their optimization variables in parallel by solving a sequence of strongly convex subproblems one for each user almost sure convergence to stationary points is proved we then customize the algorithmic framework to solve the stochastic sum rate maximization problem over single input single output siso frequency selective interference channels multiple input multiple output mimo interference channels and mimo multiple access channels numerical results corroborate that the proposed algorithms can converge faster than state of the art stochastic gradient schemes while achieving the same or better sum rates

statistical inference for the population landscape via moment adjusted stochastic gradients modern statistical inference tasks often require iterative optimization methods to compute the solution convergence analysis from an optimization viewpoint informs us only how well the solution is approximated numerically but overlooks the sampling nature of the data in contrast recognizing the randomness in the data statisticians are keen to provide uncertainty quantification or confidence for the solution obtained by using iterative optimization methods the paper makes progress along this direction by introducing moment adjusted stochastic gradient descent a new stochastic optimization method for statistical inference we establish non asymptotic theory that characterizes the statistical distribution for certain iterative methods with optimization guarantees on the statistical front the theory allows for model misspecification with very mild conditions on the data for optimization the theory is flexible for both convex and non convex cases remarkably the moment adjusting idea motivated from error standardization in statistics achieves a similar effect to acceleration in first order optimization methods that are used to fit generalized linear models we also demonstrate this acceleration effect in the non convex setting through numerical experiments

integral analysis method iam this paper presents the theoretical foundations of the new integral analysis method iam and its application to a facility location problem this methodology integrates the cardinal and ordinal criteria of combinatorial stochastic optimization problems in four stages definition of the problem cardinal analysis ordinal analysis and integration analysis the method uses the concepts of stochastic multicriteria acceptability analysis smaa monte carlo simulation optimization techniques and elements of probability the proposed method iam was used to determine optimal locations for the retail stores of a colombian coffee marketing company

adaptive stochastic approximation by the simultaneous perturbation method stochastic approximation sa has long been applied for problems of minimizing loss functions or root finding with noisy input information as with all stochastic search algorithms there are adjustable algorithm coefficients that must be specified and that can have a profound effect on algorithm performance it is known that choosing these coefficients according to an sa analog of the deterministic newton raphson algorithm provides an optimal or near optimal form of the algorithm however directly determining the required hessian matrix or jacobian matrix for root finding to achieve this algorithm form has often been difficult or impossible in practice the paper presents a general adaptive sa algorithm that is based on a simple method for estimating the hessian matrix while concurrently estimating the primary parameters of interest the approach applies in both the gradient free optimization kiefer wolfowitz and root finding stochastic gradient based robbins monro settings and is based on the simultaneous perturbation sp idea introduced previously the algorithm requires only a small number of loss function or gradient measurements per iteration independent of the problem dimension to adaptively estimate the hessian and parameters of primary interest aside from introducing the adaptive sp approach the paper presents practical implementation guidance asymptotic theory and a nontrivial numerical evaluation also included is a discussion and numerical analysis comparing the adaptive sp approach with the iterate averaging approach to accelerated sa

on stochastic gradient and subgradient methods with adaptive steplength sequences traditionally stochastic approximation sa schemes have been popular choices for solving stochastic optimization problems however the performance of standard sa implementations can vary significantly based on the choice of the steplength sequence and in general little guidance is provided about good choices motivated by this gap we present two adaptive steplength schemes for strongly convex differentiable stochastic optimization problems equipped with convergence theory that aim to overcome some of the reliance on user specific parameters the first scheme referred to as a recursive steplength stochastic approximation rsa scheme optimizes the error bounds to derive a rule that expresses the steplength at a given iteration as a simple function of the steplength at the previous iteration and certain problem parameters the second scheme termed as a cascading steplength stochastic approximation csa scheme maintains the steplength sequence as a piecewise constant decreasing function with the reduction in the steplength occurring when a suitable error threshold is met then we allow for nondifferentiable objectives but with bounded subgradients over a certain domain in such a regime we propose a local smoothing technique based on random local perturbations of the objective function that leads to a differentiable approximation of the function assuming a uniform distribution on the local randomness we establish a lipschitzian property for the gradient of the approximation and prove that the obtained lipschitz bound grows at a modest rate with problem size this facilitates the development of an adaptive steplength stochastic approximation framework which now requires sampling in the product space of the original measure and the artificially introduced distribution

convergence and rate of convergence of a recursive identification and adaptive control method which uses truncated estimators a stochastic approximation like method is used for the recursive identification of the coefficients in y n sum min 1 max l 1 a i y n i sum min 0 max l 2 b i u n i sum min 1 max l 3 c i w n i w n where w n is a sequence of mutually independent and bounded random variables and is independent of the bounded u n such methods normally require the recursive estimation of the residuals or the w n and the algorithms for doing this can be unstable if the parameter estimates are not close enough to their true values the problem is solved here by use of a simple truncated estimator which is probably what would be used in implementation in any case then under a stability and strict positive real type condition with probability 1 w p 1 convergence is proved and the rate of convergence is obtained an associated adaptive control problem is also treated

on projected stochastic gradient descent algorithm with weighted averaging for least squares regression the problem of least squares regression of a d dimensional unknown parameter is considered a stochastic gradient descent based algorithm with weighted iterate averaging that uses a single pass over the data is studied and its convergence rate is analyzed we first consider a bounded constraint set of the unknown parameter under some standard regularity assumptions we provide an explicit o 1 k upper bound on the convergence rate depending on the variance due to the additive noise in the measurements and the size of the constraint set we show that the variance term dominates the error and decreases with rate 1 k while the term that is related to the size of the constraint set decreases with rate log k k 2 we then compare the asymptotic ratio rho between the convergence rate of the proposed scheme and the empirical risk minimizer erm as the number of iterations approaches infinity we show that rho leq 4 for all d geq 1 when the random entries of the sensing vector are uncorrelated and identically distributed we further improve the upper bound by showing that rho leq 4 3 for the case of d 1 and unbounded parameter set when the random sensing entries are equal across time simulation results demonstrate strong performance of the algorithm as compared to existing methods and coincide with rho leq 4 3 even for large d in practice

adaptive estimation of hmm transition probabilities this paper presents new schemes for recursive estimation of the state transition probabilities for hidden markov models hmms via extended least squares els and recursive state prediction error rspe methods local convergence analysis for the proposed rspe algorithm is shown using the ordinary differential equation ode approach developed for the more familiar recursive output prediction error rpe methods the presented scheme converges and is relatively well conditioned compared with the previously proposed rpe scheme for estimating the transition probabilities that perform poorly in low noise the els algorithm presented is computationally of order n sup 2 which is less than the computational effort of order n sup 4 required to implement the rspe and previous rpe scheme where n is the number of markov states building on earlier work an algorithm for simultaneous estimation of the state output mappings and the state transition probabilities that requires less computational effort than earlier schemes is also presented and discussed implementation aspects of the proposed algorithms are discussed and simulation studies are presented to illustrate the convergence and convergence rates

rough sets theory for multicriteria decision analysis the original rough set approach proved to be very useful in dealing with inconsistency problems following from information granulation it operates on a data table composed of a set u of objects actions described by a set q of attributes its basic notions are indiscernibility relation on u lower and upper approximation of either a subset or a partition of u dependence and reduction of attributes from q and decision rules derived from lower approximations and boundaries of subsets identified with decision classes the original rough set idea is failing however when preference orders of attribute domains criteria are to be taken into account precisely it cannot handle inconsistencies following from violation of the dominance principle this inconsistency is characteristic for preferential information used in multicriteria decision analysis mcda problems like sorting choice or ranking in order to deal with this kind of inconsistency a number of methodological changes to the original rough sets theory is necessary the main change is the substitution of the indiscernibility relation by a dominance relation which permits approximation of ordered sets in multicriteria sorting to approximate preference relations in multicriteria choice and ranking problems another change is necessary substitution of the data table by a pairwise comparison table where each row corresponds to a pair of objects described by binary relations on particular criteria in all those mcda problems the new rough set approach ends with a set of decision rules playing the role of a comprehensive preference model it is more general than the classical functional or relational model and it is more understandable for the users because of its natural syntax in order to workout a recommendation in one of the mcda problems we propose exploitation procedures of the set of decision rules finally some other recently obtained results are given rough approximations by means of similarity relations rough set handling of missing data comparison of the rough set model with sugeno and choquet integrals and results on equivalence of a decision rule preference model and a conjoint measurement model which is neither additive nor transitive

on robustness to noise of least squares based adaptive control abstract current engineering practice for adaptive control schemes is to base the design on globally convergent schemes for simple plant models an important class of such schemes uses least squares estimation of assumed simple input output models and constructs the controller using the parameter estimates this paper studies the robustness of such schemes to the presence of unmodelled plant coloured noise such noise is sometimes an adequate model for unmodelled plant dynamics the theory of the paper makes a connection between the least squares parameter error equations and those associated with extended least squares using a posteriori noise estimates for which there are known global convergence results for the case of adaptive minimum variance control of minimum phase plants this connection permits stronger convergence results than those hitherto derived from the theory of extended least squares based on a priori noise estimates

smaa stochastic multiobjective acceptability analysis stochastic multiobjective acceptability analysis smaa is a multicriteria decision support technique for multiple decision makers based on exploring the weight space inaccurate or uncertain input data can be represented as probability distributions in smaa the decision makers need not express their preferences explicitly or implicitly instead the technique analyses what kind of valuations would make each alternative the preferred one the method produces for each alternative an acceptability index measuring the variety of different valuations that support that alternative a central weight vector representing the typical valuations resulting in that decision and a confidence factor measuring whether the input data is accurate enough for making an informed decision

the late acceptance hill climbing heuristic abstract this paper introduces a new and very simple search methodology called late acceptance hill climbing lahc it is a local search algorithm which accepts non improving moves when a candidate cost function is better than it was a number of iterations before this number appears as a single algorithmic input parameter which determines the total processing time of the search procedure the properties of this method are experimentally studied in this paper with a range of travelling salesman and exam timetabling benchmark problems also we present a fair comparison of lahc with well known search techniques which employ a cooling schedule simulated annealing sa threshold accepting ta and the great deluge algorithm gda in addition we discuss the success of the method in winning an international competition to automatically solve the magic square problem our experiments have shown that the lahc approach is simple easy to implement and yet is an effective search procedure for most of the studied instances especially for the large sized ones its average performance is better than competitor methods moreover the lahc approach has an additional advantage in contrast to the above cooling schedule based methods in its scale independence we present an example where the rescaling of a cost function in the travelling salesman problem dramatically deteriorates the performance of three cooling schedule based techniques but has absolutely no influence upon the performance of lahc

acceleration of stochastic approximation by averaging a new recursive algorithm of stochastic approximation type with the averaging of trajectories is investigated convergence with probability one is proved for a variety of classical optimization and identification problems it is also demonstrated for these problems that the proposed algorithm achieves the highest possible rate of convergence

stochastic root finding and efficient estimation of convex risk measures reliable risk measurement is a key problem for financial institutions and regulatory authorities the current industry standard value at risk has several deficiencies improved risk measures have been suggested and analyzed in the recent literature but their computational implementation has largely been neglected so far we propose and investigate stochastic approximation algorithms for the convex risk measure utility based shortfall risk our approach combines stochastic root finding schemes with importance sampling we prove that the resulting shortfall risk estimators are consistent and asymptotically normal and provide formulas for confidence intervals the performance of the proposed algorithms is tested numerically we finally apply our techniques to the normal copula model which is also known as the industry model creditmetrics this provides guidance for future implementations in practice

on complexity issues of online learning algorithms in this paper some new probabilistic upper bounds are presented for the online learning algorithm proposed in and more generally for linear stochastic approximations in hilbert spaces with these upper bounds not only does one recover almost sure convergence but also relaxes the square summable condition on the step size appeared in the early work furthermore two probabilistic upper bounds are given for an averaging process both of which achieve the same rate with respect to sample size as in batch learning algorithms and one of which is tight in both sample size and regularization parameter

manifold identification in dual averaging for regularized stochastic online learning iterative methods that calculate their steps from approximate subgradient directions have proved to be useful for stochastic learning problems over large and streaming data sets when the objective consists of a loss function plus a nonsmooth regularization term the solution often lies on a low dimensional manifold of parameter space along which the regularizer is smooth when an l1 regularizer is used to induce sparsity in the solution for example this manifold is defined by the set of nonzero components of the parameter vector this paper shows that a regularized dual averaging algorithm can identify this manifold with high probability before reaching the solution this observation motivates an algorithmic strategy in which once an iterate is suspected of lying on an optimal or near optimal manifold we switch to a local phase that searches in this manifold thus converging rapidly to a near optimal point computational results are presented to verify the identification property and to illustrate the effectiveness of this approach

adaptive control of nonminimum phase systems recent papers have established global convergence for a class of adaptive control algorithms for discrete time linear dynamic systems however in most cases studied to date it has been assumed that the system is stably invertible this assumption plays a major role in the proofs of convergence in this paper we consider the more general case in which it is not assumed that the system is either stable or stably invertible we establish local convergence for a class of adaptive control algorithms applied to general discrete deterministic linear time invariant systems by convergence in this context we mean that the system inputs and outputs remain bounded for all time and the closed loop poles are effectively assigned in the limit for a given desired trajectory

combining monte carlo and mean field like methods for inference in hidden markov random fields issues involving missing data are typical settings where exact inference is not tractable as soon as nontrivial interactions occur between the missing variables approximations are required and most of them are based either on simulation methods or on deterministic variational methods while variational methods provide fast and reasonable approximate estimates in many scenarios simulation methods offer more consideration of important theoretical issues such as accuracy of the approximation and convergence of the algorithms but at a much higher computational cost in this work we propose a new class of algorithms that combine the main features and advantages of both simulation and deterministic methods and consider applications to inference in hidden markov random fields hmrfs these algorithms can be viewed as stochastic perturbations of variational expectation maximization vem algorithms which are not tractable for hmrf we focus more specifically on one of these perturbations and we prove their almost sure convergence to the same limit set as the limit set of vem in addition experiments on synthetic and real world images show that the algorithm performance is very close and sometimes better than that of other existing simulation based and variational em like algorithms

on adaptive hmm state estimation new online adaptive hidden markov model hmm state estimation schemes are developed based on extended least squares els concepts and recursive prediction error rpe methods the best of the new schemes exploit the idempotent nature of markov chains and work with a least squares prediction error index using a posterior estimates more suited to markov models than traditionally used in identification of linear systems these new schemes learn the set of n markov chain states and the a posteriori probability of being in each of the states at each time instant they are designed to achieve the strengths in terms of computational effort and convergence rates of each of the two classes of earlier proposed adaptive hmm schemes without the weaknesses of each in these areas the computational effort is of order n implementation aspects of the proposed algorithms are discussed and simulation studies are presented to illustrate convergence rates in comparison to earlier proposed online schemes

on closed loop adaptive noise cancellation given the mean limit ordinary differential equation for the stochastic approximation defining the adaptive algorithm for a closed loop adaptive noise cancellation we characterize the limit points under appropriate conditions it is shown that as the dimension of the weight vector increases the sequence of corresponding limit points converges in the sense of l sub 2 to the infinite dimensional optimal weight vector also the limit point of the algorithm is nearly optimal if the dimension of the weight vector is large enough the gradient of the mean square error with respect to the weight vector evaluated at the limit goes to zero in l sub 1 and l sub 2 as the dimension increases as does the gradient with respect to the coefficients in the transfer function connecting the reference noise signal with the error output thus the algorithm is nearly a gradient descent algorithm and is error reducing for large enough dimension under broad conditions iterative averaging can be used to get a nearly optimal rate of convergence

on line estimation of hidden markov model parameters based on the kullback leibler information measure sequential or online hidden markov model hmm signal processing schemes are derived and their performance is illustrated by simulation the online algorithms are sequential expectation maximization em schemes and are derived by using stochastic approximations to maximize the kullback leibler information measure the schemes can be implemented either as filters or fixed lag or sawtooth lag smoothers they yield estimates of the hmm parameters including transition probabilities markov state levels and noise variance in contrast to the offline em algorithm baum welch scheme which uses the fixed interval forward backward scheme the online schemes have significantly reduced memory requirements and improved convergence and they can estimate hmm parameters that vary slowly with time or undergo infrequent jump changes similar techniques are used to derive online schemes for extracting finite state markov chains imbedded in a mixture of white gaussian noise wgn and deterministic signals of known functional form with unknown parameters