A number of representation schemes have been presented for use within Learning Classifier Systems, ranging from binary encodings to Neural Networks, and more recently Dynamical Genetic Programming (DGP). This paper presents results from an investigation into using a fuzzy DGP representation within the XCSF Learning Classifier System. In particular, asynchronous Fuzzy Logic Networks are used to represent the traditional condition-action production system rules. It is shown possible to use self-adaptive, open-ended evolution to design an ensemble of such fuzzy dynamical systems within XCSF to solve several well-known continuous-valued test problems.

A major challenge in single particle reconstruction from cryo-electron microscopy is to establish a reliable ab-initio three-dimensional model using two-dimensional projection images with unknown orientations. Common-lines based methods estimate the orientations without additional geometric information. However, such methods fail when the detection rate of common-lines is too low due to the high level of noise in the images. An approximation to the least squares global self consistency error was obtained using convex relaxation by semidefinite programming. In this paper we introduce a more robust global self consistency error and show that the corresponding optimization problem can be solved via semidefinite relaxation. In order to prevent artificial clustering of the estimated viewing directions, we further introduce a spectral norm term that is added as a constraint or as a regularization term to the relaxed minimization problem. The resulted problems are solved by using either the alternating direction method of multipliers or an iteratively reweighted least squares procedure. Numerical experiments with both simulated and real images demonstrate that the proposed methods significantly reduce the orientation estimation error when the detection rate of common-lines is low.

Several key issues arise in implementing computer vision recognition of world objects in terms of Bayesian networks. Computational efficiency is a driving force. Perceptual networks are very deep, typically fifteen levels of structure. Images are wide, e.g., an unspecified-number of edges may appear anywhere in an image 512 x 512 pixels or larger. For efficiency, we dynamically instantiate hypotheses of observed objects. The network is not fixed, but is created incrementally at runtime. Generation of hypotheses of world objects and indexing of models for recognition are important, but they are not considered here [4,11]. This work is aimed at near-term implementation with parallel computation in a radar surveillance system, ADRIES [5, 15], and a system for industrial part recognition, SUCCESSOR [2]. For many applications, vision must be faster to be practical and so efficiently controlling the machine vision process is critical. Perceptual operators may scan megapixels and may require minutes of computation time. It is necessary to avoid unnecessary sensor actions and computation. Parallel computation is available at several levels of processor capability. The potential for parallel, distributed computation for high-level vision means distributing non-homogeneous computations. This paper addresses the problem of task control in machine vision systems based on Bayesian probability models. We separate control and inference to extend the previous work [3] to maximize utility instead of probability. Maximizing utility allows adopting perceptual strategies for efficient information gathering with sensors and analysis of sensor data. Results of controlling machine vision via utility to recognize military situations are presented in this paper. Future work extends this to industrial part recognition for SUCCESSOR.

Albeit, the implicit feedback based recommendation problem - when only the user history is available but there are no ratings - is the most typical setting in real-world applications, it is much less researched than the explicit feedback case. State-of-the-art algorithms that are efficient on the explicit case cannot be straightforwardly transformed to the implicit case if scalability should be maintained. There are few if any implicit feedback benchmark datasets, therefore new ideas are usually experimented on explicit benchmarks. In this paper, we propose a generic context-aware implicit feedback recommender algorithm, coined iTALS. iTALS apply a fast, ALS-based tensor factorization learning method that scales linearly with the number of non-zero elements in the tensor. The method also allows us to incorporate diverse context information into the model while maintaining its computational efficiency. In particular, we present two such context-aware implementation variants of iTALS. The first incorporates seasonality and enables to distinguish user behavior in different time intervals. The other views the user history as sequential information and has the ability to recognize usage pattern typical to certain group of items, e.g. to automatically tell apart product types or categories that are typically purchased repetitively (collectibles, grocery goods) or once (household appliances). Experiments performed on three implicit datasets (two proprietary ones and an implicit variant of the Netflix dataset) show that by integrating context-aware information with our factorization framework into the state-of-the-art implicit recommender algorithm the recommendation quality improves significantly.

Non-convex sparsity-inducing penalties have recently received considerable attentions in sparse learning. Recent theoretical investigations have demonstrated their superiority over the convex counterparts in several sparse learning settings. However, solving the non-convex optimization problems associated with non-convex penalties remains a big challenge. A commonly used approach is the Multi-Stage (MS) convex relaxation (or DC programming), which relaxes the original non-convex problem to a sequence of convex problems. This approach is usually not very practical for large-scale problems because its computational cost is a multiple of solving a single convex problem. In this paper, we propose a General Iterative Shrinkage and Thresholding (GIST) algorithm to solve the nonconvex optimization problem for a large class of non-convex penalties. The GIST algorithm iteratively solves a proximal operator problem, which in turn has a closed-form solution for many commonly used penalties. At each outer iteration of the algorithm, we use a line search initialized by the Barzilai-Borwein (BB) rule that allows finding an appropriate step size quickly. The paper also presents a detailed convergence analysis of the GIST algorithm. The efficiency of the proposed algorithm is demonstrated by extensive experiments on large-scale data sets.

Nonnegative matrix factorization (NMF) has become a ubiquitous tool for data analysis. An important variant is the sparse NMF problem which arises when we explicitly require the learnt features to be sparse. A natural measure of sparsity is the L$_0$ norm, however its optimization is NP-hard. Mixed norms, such as L$_1$/L$_2$ measure, have been shown to model sparsity robustly, based on intuitive attributes that such measures need to satisfy. This is in contrast to computationally cheaper alternatives such as the plain L$_1$ norm. However, present algorithms designed for optimizing the mixed norm L$_1$/L$_2$ are slow and other formulations for sparse NMF have been proposed such as those based on L$_1$ and L$_0$ norms. Our proposed algorithm allows us to solve the mixed norm sparsity constraints while not sacrificing computation time. We present experimental evidence on real-world datasets that shows our new algorithm performs an order of magnitude faster compared to the current state-of-the-art solvers optimizing the mixed norm and is suitable for large-scale datasets.

We present an approach to decomposition and factor analysis of matrices with ordinal data. The matrix entries are grades to which objects represented by rows satisfy attributes represented by columns, e.g. grades to which an image is red, a product has a given feature, or a person performs well in a test. We assume that the grades form a bounded scale equipped with certain aggregation operators and conforms to the structure of a complete residuated lattice. We present a greedy approximation algorithm for the problem of decomposition of such matrix in a product of two matrices with grades under the restriction that the number of factors be small. Our algorithm is based on a geometric insight provided by a theorem identifying particular rectangular-shaped submatrices as optimal factors for the decompositions. These factors correspond to formal concepts of the input data and allow an easy interpretation of the decomposition. We present illustrative examples and experimental evaluation.

We propose a new method to enforce priors on the solution of the nonnegative matrix factorization (NMF). The proposed algorithm can be used for denoising or single-channel source separation (SCSS) applications. The NMF solution is guided to follow the Minimum Mean Square Error (MMSE) estimates under Gaussian mixture prior models (GMM) for the source signal. In SCSS applications, the spectra of the observed mixed signal are decomposed as a weighted linear combination of trained basis vectors for each source using NMF. In this work, the NMF decomposition weight matrices are treated as a distorted image by a distortion operator, which is learned directly from the observed signals. The MMSE estimate of the weights matrix under GMM prior and log-normal distribution for the distortion is then found to improve the NMF decomposition results. The MMSE estimate is embedded within the optimization objective to form a novel regularized NMF cost function. The corresponding update rules for the new objectives are derived in this paper. Experimental results show that, the proposed regularized NMF algorithm improves the source separation performance compared with using NMF without prior or with other prior models.

This paper proposes a method to find the actual state of a complex dynamic system from information coming from the sensors on the system himself, or on its environment. The nominal evolution of the system is a priori known and can be modeled (by an expert, for example), by different methods. In this paper, the Petri nets have been chosen. Contrary to the usual use of the Petri nets, the initial state of the system is unknown. So a degree of belief is bound to each places, or set of places. The theory used to model this uncertainty is the Dempster-Shafer's one which is well adapted to this type of problems. From the given Petri net characterizing the nominal evolution of the dynamic system, and from the observation inputs, the proposed method allows to determine according to the reliability of the model and the inputs, the state of the system at any time.

A control algorithm for batch processing of mixed waste is proposed based on conditional Gaussian Bayesian networks. The network is compiled during batch staging for real-time response to sensor input.

Reactive (memoryless) policies are sufficient in completely observable Markov decision processes (MDPs), but some kind of memory is usually necessary for optimal control of a partially observable MDP. Policies with finite memory can be represented as finite-state automata. In this paper, we extend Baird and Moore's VAPS algorithm to the problem of learning general finite-state automata. Because it performs stochastic gradient descent, this algorithm can be shown to converge to a locally optimal finite-state controller. We provide the details of the algorithm and then consider the question of under what conditions stochastic gradient descent will outperform exact gradient descent. We conclude with empirical results comparing the performance of stochastic and exact gradient descent, and showing the ability of our algorithm to extract the useful information contained in the sequence of past observations to compensate for the lack of observability at each time-step.

Transformation groups, such as translations or rotations, effectively express part of the variability observed in many recognition problems. The group structure enables the construction of invariant signal representations with appealing mathematical properties, where convolutions, together with pooling operators, bring stability to additive and geometric perturbations of the input. Whereas physical transformation groups are ubiquitous in image and audio applications, they do not account for all the variability of complex signal classes. We show that the invariance properties built by deep convolutional networks can be cast as a form of stable group invariance. The network wiring architecture determines the invariance group, while the trainable filter coefficients characterize the group action. We give explanatory examples which illustrate how the network architecture controls the resulting invariance group. We also explore the principle by which additional convolutional layers induce a group factorization enabling more abstract, powerful invariant representations.

Planning problems are hard, motion planning, for example, isPSPACE-hard. Such problems are even more difficult in the presence of uncertainty. Although, Markov Decision Processes (MDPs) provide a formal framework for such problems, finding solutions to high dimensional continuous MDPs is usually difficult, especially when the actions and time measurements are continuous. Fortunately, problem-specific knowledge allows us to design controllers that are good locally, though having no global guarantees. We propose a method of nonparametrically combining local controllers to obtain globally good solutions. We apply this formulation to two types of problems : motion planning (stochastic shortest path) and discounted MDPs. For motion planning, we argue that usual MDP optimality criterion (expected cost) may not be practically relevant. Wepropose an alternative: finding the minimum cost path,subject to the constraint that the robot must reach the goal withhigh probability. For this problem, we prove that a polynomial number of samples is sufficient to obtain a high probability path. For discounted MDPs, we propose a formulation that explicitly deals with model uncertainty, i.e., the problem introduced when transition probabilities are not known exactly. We formulate the problem as a robust linear program which directly incorporates this type of uncertainty.

Filtering---estimating the state of a partially observable Markov process from a sequence of observations---is one of the most widely studied problems in control theory, AI, and computational statistics. Exact computation of the posterior distribution is generally intractable for large discrete systems and for nonlinear continuous systems, so a good deal of effort has gone into developing robust approximation algorithms. This paper describes a simple stochastic approximation algorithm for filtering called {em decayed MCMC}. The algorithm applies Markov chain Monte Carlo sampling to the space of state trajectories using a proposal distribution that favours flips of more recent state variables. The formal analysis of the algorithm involves a generalization of standard coupling arguments for MCMC convergence. We prove that for any ergodic underlying Markov process, the convergence time of decayed MCMC with inverse-polynomial decay remains bounded as the length of the observation sequence grows. We show experimentally that decayed MCMC is at least competitive with other approximation algorithms such as particle filtering.

This paper presents a model based on an hybrid system to numerically simulate the climbing phase of an aircraft. This model is then used within a trajectory prediction tool. Finally, the Covariance Matrix Adaptation Evolution Strategy (CMA-ES) optimization algorithm is used to tune five selected parameters, and thus improve the accuracy of the model. Incorporated within a trajectory prediction tool, this model can be used to derive the order of magnitude of the prediction error over time, and thus the domain of validity of the trajectory prediction. A first validation experiment of the proposed model is based on the errors along time for a one-time trajectory prediction at the take off of the flight with respect to the default values of the theoretical BADA model. This experiment, assuming complete information, also shows the limit of the model. A second experiment part presents an on-line trajectory prediction, in which the prediction is continuously updated based on the current aircraft position. This approach raises several issues, for which improvements of the basic model are proposed, and the resulting trajectory prediction tool shows statistically significantly more accurate results than those of the default model.

Nowadays, huge efforts are made to modernize the air traffic management systems to cope with uncertainty, complexity and sub-optimality. An answer is to enhance the information sharing between the stakeholders. This paper introduces a framework that bridges the gap between air traffic management and air traffic control on the one hand, and bridges the gap between the ground, the approach and the en-route centers on the other hand. An original system is presented, that has three essential components: the trajectory models, the optimization process, and the monitoring process. The uncertainty of the trajectory is modeled with a Bayesian Network, where the nodes are associated to two types of random variables: the time of overflight on metering points of the airspace, and the traveling time of the routes linking these points. The resulting Bayesian Network covers the complete airspace, and Monte- Carlo simulations are done to estimate the probabilities of sector congestion and delays. On top of this trajectory model, an optimization process minimizes these probabilities by tuning the parameters of the Bayesian trajectory model related to overflight times on metering points. The last component is the monitoring process, that continuously updates the situation of the airspace, modifying the trajectories uncertainties according to actual positions of aircraft. After each update, a new optimal set of overflight times is computed, and can be communicated to the controllers as clearances for the aircraft pilots. The paper presents a formal specification of this global optimization problem, whose underlying rationale was derived with the help of air traffic controllers at Thales Air Systems.

Group elevator scheduling is an NP-hard sequential decision-making problem with unbounded state spaces and substantial uncertainty. Decision-theoretic reasoning plays a surprisingly limited role in fielded systems. A new opportunity for probabilistic methods has opened with the recent discovery of a tractable solution for the expected waiting times of all passengers in the building, marginalized over all possible passenger itineraries. Though commercially competitive, this solution does not contemplate future passengers. Yet in up-peak traffic, the effects of future passengers arriving at the lobby and entering elevator cars can dominate all waiting times. We develop a probabilistic model of how these arrivals affect the behavior of elevator cars at the lobby, and demonstrate how this model can be used to very significantly reduce the average waiting time of all passengers.

This paper presents a scalable control algorithm that enables a deployed mobile robot system to make high-level decisions under full consideration of its probabilistic belief. Our approach is based on insights from the rich literature of hierarchical controllers and hierarchical MDPs. The resulting controller has been successfully deployed in a nursing facility near Pittsburgh, PA. To the best of our knowledge, this work is a unique instance of applying POMDPs to high-level robotic control problems.

The task of estimating the gradient of a function in the presence of noise is central to several forms of reinforcement learning, including policy search methods. We present two techniques for reducing gradient estimation errors in the presence of observable input noise applied to the control signal. The first method extends the idea of a reinforcement baseline by fitting a local linear model to the function whose gradient is being estimated; we show how to find the linear model that minimizes the variance of the gradient estimate, and how to estimate the model from data. The second method improves this further by discounting components of the gradient vector that have high variance. These methods are applied to the problem of motor control learning, where actuator noise has a significant influence on behavior. In particular, we apply the techniques to learn locally optimal controllers for a dart-throwing task using a simulated three-link arm; we demonstrate that proposed methods significantly improve the reward function gradient estimate and, consequently, the learning curve, over existing methods.

In 1950, Forsythe and Leibler (1950) introduced a statistical technique for finding the inverse of a matrix by characterizing the elements of the matrix inverse as expected values of a sequence of random walks. Barto and Duff (1994) subsequently showed relations between this technique and standard dynamic programming and temporal differencing methods. The advantage of the Monte Carlo matrix inversion (MCMI) approach is that it scales better with respect to state-space size than alternative techniques. In this paper, we introduce an algorithm for performing reinforcement learning policy evaluation using MCMI. We demonstrate that MCMI improves on runtime over a maximum likelihood model-based policy evaluation approach and on both runtime and accuracy over the temporal differencing (TD) policy evaluation approach. We further improve on MCMI policy evaluation by adding an importance sampling technique to our algorithm to reduce the variance of our estimator. Lastly, we illustrate techniques for scaling up MCMI to large state spaces in order to perform policy improvement.

Recent attempts to automate business processes and medical-treatment processes have uncovered the need for a formal framework that can accommodate not only temporal constraints, but also observations and actions with uncontrollable durations. To meet this need, this paper defines a Conditional Simple Temporal Network with Uncertainty (CSTNU) that combines the simple temporal constraints from a Simple Temporal Network (STN) with the conditional nodes from a Conditional Simple Temporal Problem (CSTP) and the contingent links from a Simple Temporal Network with Uncertainty (STNU). A notion of dynamic controllability for a CSTNU is defined that generalizes the dynamic consistency of a CTP and the dynamic controllability of an STNU. The paper also presents some sound constraint-propagation rules for dynamic controllability that are expected to form the backbone of a dynamic-controllability-checking algorithm for CSTNUs.

Many problems in sequential decision making and stochastic control often have natural multiscale structure: sub-tasks are assembled together to accomplish complex goals. Systematically inferring and leveraging hierarchical structure, particularly beyond a single level of abstraction, has remained a longstanding challenge. We describe a fast multiscale procedure for repeatedly compressing, or homogenizing, Markov decision processes (MDPs), wherein a hierarchy of sub-problems at different scales is automatically determined. Coarsened MDPs are themselves independent, deterministic MDPs, and may be solved using existing algorithms. The multiscale representation delivered by this procedure decouples sub-tasks from each other and can lead to substantial improvements in convergence rates both locally within sub-problems and globally across sub-problems, yielding significant computational savings. A second fundamental aspect of this work is that these multiscale decompositions yield new transfer opportunities across different problems, where solutions of sub-tasks at different levels of the hierarchy may be amenable to transfer to new problems. Localized transfer of policies and potential operators at arbitrary scales is emphasized. Finally, we demonstrate compression and transfer in a collection of illustrative domains, including examples involving discrete and continuous statespaces.

To achieve sparse parametrizations that allows intuitive analysis, we aim to represent deformation with a basis containing interpretable elements, and we wish to use elements that have the description capacity to represent the deformation compactly. To accomplish this, we introduce in this paper higher-order momentum distributions in the LDDMM registration framework. While the zeroth order moments previously used in LDDMM only describe local displacement, the first-order momenta that are proposed here represent a basis that allows local description of affine transformations and subsequent compact description of non-translational movement in a globally non-rigid deformation. The resulting representation contains directly interpretable information from both mathematical and modeling perspectives. We develop the mathematical construction of the registration framework with higher-order momenta, we show the implications for sparse image registration and deformation description, and we provide examples of how the parametrization enables registration with a very low number of parameters. The capacity and interpretability of the parametrization using higher-order momenta lead to natural modeling of articulated movement, and the method promises to be useful for quantifying ventricle expansion and progressing atrophy during Alzheimer's disease.

This paper discusses clustering and latent semantic indexing (LSI) aspects of the singular value decomposition (SVD). The purpose of this paper is twofold. The first is to give an explanation on how and why the singular vectors can be used in clustering. And the second is to show that the two seemingly unrelated SVD aspects actually originate from the same source: related vertices tend to be more clustered in the graph representation of lower rank approximate matrix using the SVD than in the original semantic graph. Accordingly, the SVD can improve retrieval performance of an information retrieval system since queries made to the approximate matrix can retrieve more relevant documents and filter out more irrelevant documents than the same queries made to the original matrix. By utilizing this fact, we will devise an LSI algorithm that mimicks SVD capability in clustering related vertices. Convergence analysis shows that the algorithm is convergent and produces a unique solution for each input. Experimental results using some standard datasets in LSI research show that retrieval performances of the algorithm are comparable to the SVD's. In addition, the algorithm is more practical and easier to use because there is no need to determine decomposition rank which is crucial in driving retrieval performance of the SVD.

Clustering is the problem of separating a set of objects into groups (called clusters) so that objects within the same cluster are more similar to each other than to those in different clusters. Spectral clustering is a now well-known method for clustering which utilizes the spectrum of the data similarity matrix to perform this separation. Since the method relies on solving an eigenvector problem, it is computationally expensive for large datasets. To overcome this constraint, approximation methods have been developed which aim to reduce running time while maintaining accurate classification. In this article, we summarize and experimentally evaluate several approximation methods for spectral clustering. From an applications standpoint, we employ spectral clustering to solve the so-called attrition problem, where one aims to identify from a set of employees those who are likely to voluntarily leave the company from those who are not. Our study sheds light on the empirical performance of existing approximate spectral clustering methods and shows the applicability of these methods in an important business optimization related problem.

We propose a new Riemannian geometry for fixed-rank matrices that is specifically tailored to the low-rank matrix completion problem. Exploiting the degree of freedom of a quotient space, we tune the metric on our search space to the particular least square cost function. At one level, it illustrates in a novel way how to exploit the versatile framework of optimization on quotient manifold. At another level, our algorithm can be considered as an improved version of LMaFit, the state-of-the-art Gauss-Seidel algorithm. We develop necessary tools needed to perform both first-order and second-order optimization. In particular, we propose gradient descent schemes (steepest descent and conjugate gradient) and trust-region algorithms. We also show that, thanks to the simplicity of the cost function, it is numerically cheap to perform an exact linesearch given a search direction, which makes our algorithms competitive with the state-of-the-art on standard low-rank matrix completion instances.

Autonomous navigation for large Unmanned Aerial Vehicles (UAVs) is fairly straight-forward, as expensive sensors and monitoring devices can be employed. In contrast, obstacle avoidance remains a challenging task for Micro Aerial Vehicles (MAVs) which operate at low altitude in cluttered environments. Unlike large vehicles, MAVs can only carry very light sensors, such as cameras, making autonomous navigation through obstacles much more challenging. In this paper, we describe a system that navigates a small quadrotor helicopter autonomously at low altitude through natural forest environments. Using only a single cheap camera to perceive the environment, we are able to maintain a constant velocity of up to 1.5m/s. Given a small set of human pilot demonstrations, we use recent state-of-the-art imitation learning techniques to train a controller that can avoid trees by adapting the MAVs heading. We demonstrate the performance of our system in a more controlled environment indoors, and in real natural forest environments outdoors.

In this paper, we investigate the trade-off between convergence rate and computational cost when minimizing a composite functional with proximal-gradient methods, which are popular optimisation tools in machine learning. We consider the case when the proximity operator is computed via an iterative procedure, which provides an approximation of the exact proximity operator. In that case, we obtain algorithms with two nested loops. We show that the strategy that minimizes the computational cost to reach a solution with a desired accuracy in finite time is to set the number of inner iterations to a constant, which differs from the strategy indicated by a convergence rate analysis. In the process, we also present a new procedure called SIP (that is Speedy Inexact Proximal-gradient algorithm) that is both computationally efficient and easy to implement. Our numerical experiments confirm the theoretical findings and suggest that SIP can be a very competitive alternative to the standard procedure.

In spectral clustering, one defines a similarity matrix for a collection of data points, transforms the matrix to get the Laplacian matrix, finds the eigenvectors of the Laplacian matrix, and obtains a partition of the data using the leading eigenvectors. The last step is sometimes referred to as rounding, where one needs to decide how many leading eigenvectors to use, to determine the number of clusters, and to partition the data points. In this paper, we propose a novel method for rounding. The method differs from previous methods in three ways. First, we relax the assumption that the number of clusters equals the number of eigenvectors used. Second, when deciding the number of leading eigenvectors to use, we not only rely on information contained in the leading eigenvectors themselves, but also use subsequent eigenvectors. Third, our method is model-based and solves all the three subproblems of rounding using a class of graphical models called latent tree models. We evaluate our method on both synthetic and real-world data. The results show that our method works correctly in the ideal case where between-clusters similarity is 0, and degrades gracefully as one moves away from the ideal case.

When data is sampled from an unknown subspace, principal component analysis (PCA) provides an effective way to estimate the subspace and hence reduce the dimension of the data. At the heart of PCA is the Eckart-Young-Mirsky theorem, which characterizes the best rank k approximation of a matrix. In this paper, we prove a generalization of the Eckart-Young-Mirsky theorem under all unitarily invariant norms. Using this result, we obtain closed-form solutions for a set of rank/norm regularized problems, and derive closed-form solutions for a general class of subspace clustering problems (where data is modelled by unions of unknown subspaces). From these results we obtain new theoretical insights and promising experimental results.