Bayesian network structure learning is the notoriously difficult problem of discovering a Bayesian network that optimally represents a given set of training data. In this paper we study the computational worst-case complexity of exact Bayesian network structure learning under graph theoretic restrictions on the (directed) super-structure. The super-structure is an undirected graph that contains as subgraphs the skeletons of solution networks. We introduce the directed super-structure as a natural generalization of its undirected counterpart. Our results apply to several variants of score-based Bayesian network structure learning where the score of a network decomposes into local scores of its nodes. Results: We show that exact Bayesian network structure learning can be carried out in non-uniform polynomial time if the super-structure has bounded treewidth, and in linear time if in addition the super-structure has bounded maximum degree. Furthermore, we show that if the directed super-structure is acyclic, then exact Bayesian network structure learning can be carried out in quadratic time. We complement these positive results with a number of hardness results. We show that both restrictions (treewidth and degree) are essential and cannot be dropped without loosing uniform polynomial time tractability (subject to a complexity-theoretic assumption). Similarly, exact Bayesian network structure learning remains NP-hard for "almost acyclic" directed super-structures. Furthermore, we show that the restrictions remain essential if we do not search for a globally optimal network but aim to improve a given network by means of at most k arc additions, arc deletions, or arc reversals (k-neighborhood local search).

Additive asynchronous and cyclostationary impulsive noise limits communication performance in OFDM powerline communication (PLC) systems. Conventional OFDM receivers assume additive white Gaussian noise and hence experience degradation in communication performance in impulsive noise. Alternate designs assume a parametric statistical model of impulsive noise and use the model parameters in mitigating impulsive noise. These receivers require overhead in training and parameter estimation, and degrade due to model and parameter mismatch, especially in highly dynamic environments. In this paper, we model impulsive noise as a sparse vector in the time domain without any other assumptions, and apply sparse Bayesian learning methods for estimation and mitigation without training. We propose three iterative algorithms with different complexity vs. performance trade-offs: (1) we utilize the noise projection onto null and pilot tones to estimate and subtract the noise impulses; (2) we add the information in the data tones to perform joint noise estimation and OFDM detection; (3) we embed our algorithm into a decision feedback structure to further enhance the performance of coded systems. When compared to conventional OFDM PLC receivers, the proposed receivers achieve SNR gains of up to 9 dB in coded and 10 dB in uncoded systems in the presence of impulsive noise.

We present the results of research with the goal of automatically creating a multilingual thesaurus based on the freely available resources of Wikipedia and WordNet. Our goal is to increase resources for natural language processing tasks such as machine translation targeting the Japanese-Spanish language pair. Given the scarcity of resources, we use existing English resources as a pivot for creating a trilingual Japanese-Spanish-English thesaurus. Our approach consists of extracting the translation tuples from Wikipedia, disambiguating them by mapping them to WordNet word senses. We present results comparing two methods of disambiguation, the first using VSM on Wikipedia article texts and WordNet definitions, and the second using categorical information extracted from Wikipedia, We find that mixing the two methods produces favorable results. Using the proposed method, we have constructed a multilingual Spanish-Japanese-English thesaurus consisting of 25,375 entries. The same method can be applied to any pair of languages that are linked to English in Wikipedia.

This article addresses the issue of representing electroencephalographic (EEG) signals in an efficient way. While classical approaches use a fixed Gabor dictionary to analyze EEG signals, this article proposes a data-driven method to obtain an adapted dictionary. To reach an efficient dictionary learning, appropriate spatial and temporal modeling is required. Inter-channels links are taken into account in the spatial multivariate model, and shift-invariance is used for the temporal model. Multivariate learned kernels are informative (a few atoms code plentiful energy) and interpretable (the atoms can have a physiological meaning). Using real EEG data, the proposed method is shown to outperform the classical multichannel matching pursuit used with a Gabor dictionary, as measured by the representative power of the learned dictionary and its spatial flexibility. Moreover, dictionary learning can capture interpretable patterns: this ability is illustrated on real data, learning a P300 evoked potential. Keywords: Dictionary learning, orthogonal matching pursuit, multivariate, shift-invariance, EEG, evoked potentials, P300. 1. Introduction Scalp electroencephalography (EEG) measures electrical activity produced by post-synaptic potentials of large neuronal assemblies. Although this old medical imaging technique suffers from poor spatial resolution, EEG is still widely used in medical contexts (e.g. EEG devices are relatively cheap compared to other imaging techniques (e.g. MEG, fMRI, PET), and they offer both high temporal resolution (a short period of time between two acquisitions) and very low latency (a delay between the mental task and the recording on the electrodes).

Image denoising based on a probabilistic model of local image patches has been employed by various researchers, and recently a deep (denoising) autoencoder has been proposed by Burger et al. [2012] and Xie et al. [2012] as a good model for this. In this paper, we propose that another popular family of models in the field of deep learning, called Boltzmann machines, can perform image denoising as well as, or in certain cases of high level of noise, better than denoising autoencoders. We empirically evaluate the two models on three different sets of images with different types and levels of noise. Throughout the experiments we also examine the effect of the depth of the models. The experiments confirmed our claim and revealed that the performance can be improved by adding more hidden layers, especially when the level of noise is high.

Recently, the deep-belief-networks (DBN) based voice activity detection (VAD) has been proposed. It is powerful in fusing the advantages of multiple features, and achieves the state-of-the-art performance. However, the deep layers of the DBN-based VAD do not show an apparent superiority to the shallower layers. In this paper, we propose a denoising-deep-neural-network (DDNN) based VAD to address the aforementioned problem. Specifically, we pre-train a deep neural network in a special unsupervised denoising greedy layer-wise mode, and then fine-tune the whole network in a supervised way by the common back-propagation algorithm. In the pre-training phase, we take the noisy speech signals as the visible layer and try to extract a new feature that minimizes the reconstruction cross-entropy loss between the noisy speech signals and its corresponding clean speech signals. Experimental results show that the proposed DDNN-based VAD not only outperforms the DBN-based VAD but also shows an apparent performance improvement of the deep layers over shallower layers.

Modeling spike firing assumes that spiking statistics are Poisson, but real data violates this assumption. To capture non-Poissonian features, in order to fix the inevitable inherent irregularity, researchers rescale the time axis with tedious computational overhead instead of searching for another distribution. Spikes or action potentials are precisely-timed changes in the ionic transport through synapses adjusting the synaptic weight, successfully modeled and developed as a memristor. Memristance value is multiples of initial resistance. This reminds us with the foundations of quantum mechanics. We try to quantize potential and resistance, as done with energy. After reviewing Planck curve for blackbody radiation, we propose the quantization equations. We introduce and prove a theorem that quantizes the resistance. Then we define the tyke showing its basic characteristics. Finally we give the basic transformations to model spiking and link an energy quantum to a tyke. Investigation shows how this perfectly models the neuron spiking, with over 97% match.

Covering is an important type of data structure while covering-based rough sets provide an efficient and systematic theory to deal with covering data. In this paper, we use boolean matrices to represent and axiomatize three types of covering approximation operators. First, we define two types of characteristic matrices of a covering which are essentially square boolean ones, and their properties are studied. Through the characteristic matrices, three important types of covering approximation operators are concisely equivalently represented. Second, matrix representations of covering approximation operators are used in boolean matrix decomposition. We provide a sufficient and necessary condition for a square boolean matrix to decompose into the boolean product of another one and its transpose. And we develop an algorithm for this boolean matrix decomposition. Finally, based on the above results, these three types of covering approximation operators are axiomatized using boolean matrices. In a word, this work borrows extensively from boolean matrices and present a new view to study covering-based rough sets.

We investigate the accuracy of the two most common estimators for the maximum expected value of a general set of random variables: a generalization of the maximum sample average, and cross validation. No unbiased estimator exists and we show that it is non-trivial to select a good estimator without knowledge about the distributions of the random variables. We investigate and bound the bias and variance of the aforementioned estimators and prove consistency. The variance of cross validation can be significantly reduced, but not without risking a large bias. The bias and variance of different variants of cross validation are shown to be very problem-dependent, and a wrong choice can lead to very inaccurate estimates.

Imaging devices such as telescopes and microscopes collect incoming light using lenses or mirrors of finite size. This finite size imposes a finite aperture on the light that reaches the optical system, leading to effects of diffraction. In particular, diffraction ensures that the image of a point can never be a point. For instance, an imaging system using a lens with an F -number f/D (where f is the focal length, and D is the diameter of the circular aperture) has an impulse response function (Airy disk) whose radius is 1.22λf/D on the sensor, where λ is the wave length of the light (for simplicity, assumed to be monochromatic). Another way to express the same insight uses the transfer function. For a lens focused at infinity, the transfer function is constant within a circle of radius ν 1/(2λf/D), and zero outside [23, p. 136]. This means, in a nutshell, that if we try to image a sinusoidal pattern with spatial frequency larger than ν, diffraction will annihilate that pattern. Likewise, if we decompose a general object into spatial frequencies by Fourier analysis, all components larger than ν will vanish. This article has been accepted for publication at the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), Portland, 2013.