Data sets are often modeled as point clouds in $R^D$, for $D$ large. It is often assumed that the data has some interesting low-dimensional structure, for example that of a $d$-dimensional manifold $M$, with $d$ much smaller than $D$. When $M$ is simply a linear subspace, one may exploit this assumption for encoding efficiently the data by projecting onto a dictionary of $d$ vectors in $R^D$ (for example found by SVD), at a cost $(n+D)d$ for $n$ data points. When $M$ is nonlinear, there are no "explicit" constructions of dictionaries that achieve a similar efficiency: typically one uses either random dictionaries, or dictionaries obtained by black-box optimization. In this paper we construct data-dependent multi-scale dictionaries that aim at efficient encoding and manipulating of the data. Their construction is fast, and so are the algorithms that map data points to dictionary coefficients and vice versa. In addition, data points are guaranteed to have a sparse representation in terms of the dictionary. We think of dictionaries as the analogue of wavelets, but for approximating point clouds rather than functions.

Volterra and polynomial regression models play a major role in nonlinear system identification and inference tasks. Exciting applications ranging from neuroscience to genome-wide association analysis build on these models with the additional requirement of parsimony. This requirement has high interpretative value, but unfortunately cannot be met by least-squares based or kernel regression methods. To this end, compressed sampling (CS) approaches, already successful in linear regression settings, can offer a viable alternative. The viability of CS for sparse Volterra and polynomial models is the core theme of this work. A common sparse regression task is initially posed for the two models. Building on (weighted) Lasso-based schemes, an adaptive RLS-type algorithm is developed for sparse polynomial regressions. The identifiability of polynomial models is critically challenged by dimensionality. However, following the CS principle, when these models are sparse, they could be recovered by far fewer measurements. To quantify the sufficient number of measurements for a given level of sparsity, restricted isometry properties (RIP) are investigated in commonly met polynomial regression settings, generalizing known results for their linear counterparts. The merits of the novel (weighted) adaptive CS algorithms to sparse polynomial modeling are verified through synthetic as well as real data tests for genotype-phenotype analysis.

Artificial general intelligence (AGI) refers to research aimed at tackling the full problem of artificial intelligence, that is, create truly intelligent agents. This sets it apart from most AI research which aims at solving relatively narrow domains, such as character recognition, motion planning, or increasing player satisfaction in games. But how do we know when an agent is truly intelligent? A common point of reference in the AGI community is Legg and Hutter's formal definition of universal intelligence, which has the appeal of simplicity and generality but is unfortunately incomputable. Games of various kinds are commonly used as benchmarks for "narrow" AI research, as they are considered to have many important properties. We argue that many of these properties carry over to the testing of general intelligence as well. We then sketch how such testing could practically be carried out. The central part of this sketch is an extension of universal intelligence to deal with finite time, and the use of sampling of the space of games expressed in a suitably biased game description language.

Evolutionary Multi-Objective Optimization is becoming a hot research area and quite a few papers regarding these algorithms have been published. However the role of local search techniques has not been expanded adequately. This paper studies the role of a local search technique called 2-opt for the Multi-Objective Travelling Salesman Problem (MOTSP). A new mutation operator called Jumping Gene (JG) is also used. Since 2-opt operator was intended for the single objective TSP, its domain has been expanded to MOTSP in this paper. This new technique is applied to the list of KroAB100 cities.

We present an application focused on the design of resilient long-reach passive optical networks. We specifically consider dual-parented networks whereby each customer must be connected to two metro sites via local exchange sites. An important property of such a placement is resilience to single metro node failure. The objective of the application is to determine the optimal position of a set of metro nodes such that the total optical fibre length is minimized. We prove that this problem is NP-Complete. We present two alternative combinatorial optimisation approaches to finding an optimal metro node placement using: a mixed integer linear programming (MIP) formulation of the problem; and, a hybrid approach that uses clustering as a preprocessing step. We consider a detailed case-study based on a network for Ireland. The hybrid approach scales well and finds solutions that are close to optimal, with a runtime that is two orders-of-magnitude better than the MIP model.

Texture classification became one of the problems which has been paid much attention on by image processing scientists since late 80s. Consequently, since now many different methods have been proposed to solve this problem. In most of these methods the researchers attempted to describe and discriminate textures based on linear and non-linear patterns. The linear and non-linear patterns on any window are based on formation of Grain Components in a particular order. Grain component is a primitive unit of morphology that most meaningful information often appears in the form of occurrence of that. The approach which is proposed in this paper could analyze the texture based on its grain components and then by making grain components histogram and extracting statistical features from that would classify the textures. Finally, to increase the accuracy of classification, proposed approach is expanded to color images to utilize the ability of approach in analyzing each RGB channels, individually. Although, this approach is a general one and it could be used in different applications, the method has been tested on the stone texture and the results can prove the quality of approach.

In this paper, we propose a novel policy iteration method, called dynamic policy programming (DPP), to estimate the optimal policy in the infinite-horizon Markov decision processes. We prove the finite-iteration and asymptotic l\infty-norm performance-loss bounds for DPP in the presence of approximation/estimation error. The bounds are expressed in terms of the l\infty-norm of the average accumulated error as opposed to the l\infty-norm of the error in the case of the standard approximate value iteration (AVI) and the approximate policy iteration (API). This suggests that DPP can achieve a better performance than AVI and API since it averages out the simulation noise caused by Monte-Carlo sampling throughout the learning process. We examine this theoretical results numerically by com- paring the performance of the approximate variants of DPP with existing reinforcement learning (RL) methods on different problem domains. Our results show that, in all cases, DPP-based algorithms outperform other RL methods by a wide margin.

The goal of machine learning is to provide solutions which are trained by data or by experience coming from the environment. Many training algorithms exist and some brilliant successes were achieved. But even in structured environments for machine learning (e.g. data mining or board games), most applications beyond the level of toy problems need careful hand-tuning or human ingenuity (i.e. detection of interesting patterns) or both. We discuss several aspects how self-configuration can help to alleviate these problems. One aspect is the self-configuration by tuning of algorithms, where recent advances have been made in the area of SPO (Sequen- tial Parameter Optimization). Another aspect is the self-configuration by pattern detection or feature construction. Forming multiple features (e.g. random boolean functions) and using algorithms (e.g. random forests) which easily digest many fea- tures can largely increase learning speed. However, a full-fledged theory of feature construction is not yet available and forms a current barrier in machine learning. We discuss several ideas for systematic inclusion of feature construction. This may lead to partly self-configuring machine learning solutions which show robustness, flexibility, and fast learning in potentially changing environments.

We propose a method for nonparametric density estimation that exhibits robustness to contamination of the training sample. This method achieves robustness by combining a traditional kernel density estimator (KDE) with ideas from classical $M$-estimation. We interpret the KDE based on a radial, positive semi-definite kernel as a sample mean in the associated reproducing kernel Hilbert space. Since the sample mean is sensitive to outliers, we estimate it robustly via $M$-estimation, yielding a robust kernel density estimator (RKDE). An RKDE can be computed efficiently via a kernelized iteratively re-weighted least squares (IRWLS) algorithm. Necessary and sufficient conditions are given for kernelized IRWLS to converge to the global minimizer of the $M$-estimator objective function. The robustness of the RKDE is demonstrated with a representer theorem, the influence function, and experimental results for density estimation and anomaly detection.

The hidden Markov model (HMM) is a generative model that treats sequential data under the assumption that each observation is conditioned on the state of a discrete hidden variable that evolves in time as a Markov chain. In this paper, we derive a novel algorithm to cluster HMMs through their probability distributions. We propose a hierarchical EM algorithm that i) clusters a given collection of HMMs into groups of HMMs that are similar, in terms of the distributions they represent, and ii) characterizes each group by a "cluster center", i.e., a novel HMM that is representative for the group. We present several empirical studies that illustrate the benefits of the proposed algorithm.