18279965
Information in the Nonstationary Case
Information estimates such as the direct method of Strong, Koberle, de Ruyter van Steveninck, and Bialek (1998) sidestep the difficult problem of estimating the joint distribution of response and stimulus by instead estimating the difference between the marginal and conditional entropies of the response. While this is an effective estimation strategy, it tempts the practitioner to ignore the role of the stimulus and the meaning of mutual information. We show here that as the number of trials increases indefinitely, the direct (or plug-in) estimate of marginal entropy converges (with probability 1) to the entropy of the time-averaged conditional distribution of the response, and the direct estimate of the conditional entropy converges to the time-averaged entropy of the conditional distribution of the response. Under joint stationarity and ergodicity of the response and stimulus, the difference of these quantities converges to the mutual information. When the stimulus is deterministic or nonstationary the direct estimate of information no longer estimates mutual information, which is no longer meaningful, but it remains a measure of variability of the response distribution across time.
2105049
Model Selection in Gaussian Graphical Models: High-Dimensional Consistency of l1-regularized MLE
We consider the problem of estimating the graph structure associated with a Gaussian Markov random field (GMRF) from i.i.d. samples. We study the performance of study the performance of thel1-regularized maximum likelihood estimator in the high-dimensional setting, where the number of nodes in the graph p, the number of edges in the graph s and the maximum node degree d, are allowed to grow as a function of the number of samples n. Our main result provides sufficient conditions on (n, p, d) for thel1-regularized MLE estimator to recover all the edges of the graph with high probability. Under some conditions on the model covariance, we show that model selection can be achieved for sample sizes n = Ω(d log(p)), with the error decaying as O(exp(−c log(p))) for some constant c. We illustrate our theoretical results via simulations and show good correspondences between the theoretical predictions and behavior in simulations.
12165073
On the Convergence of Boosting Procedures
A boosting algorithm seeks to minimize empirically a loss function in a greedy fashion. The resulted estimator takes an additive function form and is built iteratively by applying a base estimator (or learner) to updated samples depending on the previous iterations. This paper studies convergence of boosting when it is carried out over the linear span of a family of basis functions. For general loss functions, we prove the convergence of boosting's greedy optimization to the infinimum of the loss function over the linear span. As a side product, these results reveal the importance of restricting the greedy search step sizes, as known in practice through the works of Friedman and others.
116839195
Some results on empirical processes and stochastic complexity
This thesis contains two parts. In Part I, an intuitive and simple approach is used to obtain uniform convergence and Central Limit Theorems for empirical processes indexed by families of functions, for stationary mixing sequences with not too slow a $\beta$-mixing (or $\phi$-mixing) rate. The conditions imposed are in terms of random metric entropies, and the $\beta$-mixing (or $\phi$-mixing) rate. In the case of a Vapnik-Cervonenkis class, the uniform convergence result holds for any strictly stationary sequence with $\beta$-mixing (or $\phi$-mixing) rate $\beta\sb{n}$ (or $\phi\sb{n}$) = $o$($n\sp{-d}$) for some d $>$ 0, while the Central Limit Theorem requires the rate $\beta\sb{n}$ (or $\phi\sb{n}$ = $o$($n\sp{-d}$) for some d $>$ 3. 
In Part II, we use a shortest code length criterion to select the bin width of a histo-gram from a string of i.i.d. observations. Under smoothness conditions on the underlying density on (0, 1), this criterion is shown to be optimal as a code selection criterion in reaching the smallest redundancy within the class of codes under consideration. Furthermore, the criterion consistently selects the underlying density when it is uniform on (0, 1). 
Minimax lower bounds for the redundancy over many smooth families of underlying densities are also derived. In a special case, the lower bound is shown to be achieved almost surely, and in expectation, by a predictive code based on a sequence of histograms. In the case of Sobolev balls, the minimax optimal code is described and a heuristic proof is provided.
828878
Image denoising via lossy compression and wavelet thresholding
Some past work has proposed to use lossy compression to remove noise, based on the rationale that a reasonable compression method retains the dominant signal features more than the randomness of the noise. Building on this theme, we explain why compression (via coefficient quantization) is appropriate for filtering noise from signal by making the connection that quantization of transform coefficients approximates the operation of wavelet thresholding for denoising. That is, denoising is mainly due to the zero-zone and that the full precision of the thresholded coefficients is of secondary importance. The method of quantization is facilitated by a criterion similar to Rissanen's minimum description length principle. An important issue is the threshold value of the zero-zone (and of wavelet thresholding). For a natural image, it has been observed that its subband coefficients can be well modeled by a Laplacian distribution. With this assumption, we derive a threshold which is easy to compute and is intuitive. Experiments show that the proposed threshold performs close to optimal thresholding.
11765401
Looking at Markov samplers through cusum path plots: a simple diagnostic idea
In this paper, we propose to monitor a Markov chain sampler using the cusum path plot of a chosen one-dimensional summary statistic. We argue that the cusum path plot can bring out, more effectively than the sequential plot, those aspects of a Markov sampler which tell the user how quickly or slowly the sampler is moving around in its sample space, in the direction of the summary statistic. The proposal is then illustrated in four examples which represent situations where the cusum path plot works well and not well. Moreover, a rigorous analysis is given for one of the examples. We conclude that the cusum path plot is an effective tool for convergence diagnostics of a Markov sampler and for comparing different Markov samplers.
34993677
Automatic text location in images and video frames
Abstract Textual data is very important in a number of applications such as image database indexing and document understanding. The goal of automatic text location without character recognition capabilities is to extract image regions that contain only text. These regions can then be either fed to an optical character recognition module or highlighted for a user. Text location is a very difficult problem because the characters in text can vary in font, size, spacing, alignment, orientation, color and texture. Further, characters are often embedded in a complex background in the image. We propose a new text location algorithm that is suitable in a number of applications, including conversion of newspaper advertisements from paper documents to their electronic versions, World Wide Web search, color image indexing and video indexing. In many of these applications, it is not necessary to extract all the text, so we emphasize on extracting important text with large size and high contrast. Our algorithm is very fast and has been shown to be successful in extracting important text in a large number of test images.
5165355
Computational prediction of novel non-coding RNAs in Arabidopsis thaliana
BackgroundNon-coding RNA (ncRNA) genes do not encode proteins but produce functional RNA molecules that play crucial roles in many key biological processes. Recent genome-wide transcriptional profiling studies using tiling arrays in organisms such as human and Arabidopsis have revealed a great number of transcripts, a large portion of which have little or no capability to encode proteins. This unexpected finding suggests that the currently known repertoire of ncRNAs may only represent a small fraction of ncRNAs of the organisms. Thus, efficient and effective prediction of ncRNAs has become an important task in bioinformatics in recent years. Among the available computational methods, the comparative genomic approach seems to be the most powerful to detect ncRNAs. The recent completion of the sequencing of several major plant genomes has made the approach possible for plants.ResultsWe have developed a pipeline to predict novel ncRNAs in the Arabidopsis (Arabidopsis thaliana) genome. It starts by comparing the expressed intergenic regions of Arabidopsis as provided in two whole-genome high-density oligo-probe arrays from the literature with the intergenic nucleotide sequences of all completely sequenced plant genomes including rice (Oryza sativa), poplar (Populus trichocarpa), grape (Vitis vinifera), and papaya (Carica papaya). By using multiple sequence alignment, a popular ncRNA prediction program (RNAz), wet-bench experimental validation, protein-coding potential analysis, and stringent screening against various ncRNA databases, the pipeline resulted in 16 families of novel ncRNAs (with a total of 21 ncRNAs).ConclusionIn this paper, we undertake a genome-wide search for novel ncRNAs in the genome of Arabidopsis by a comparative genomics approach. The identified novel ncRNAs are evolutionarily conserved between Arabidopsis and other recently sequenced plants, and may conduct interesting novel biological functions.
18656180
Application of PGA on Optimization of Distribution of Shopping Centers
In this study, the distribution of shopping centers is optimized in terms of realizing the shortest car-based shopping trips in an urban area. Modal split is performed between road and public traffic networks is calculated, and then the interaction between land-use and transportation in the context of choice of shopping destinations is modeled to build the optimal function. Parallel genetic algorithm (PGA) is applied to solve the optimal problem on distribution of the area of shopping centers. Several problems in application of PGA are discussed. A case study is undertaken in order to examine the effectiveness of this method.
10885412
Managing the pedigree and quality of information in dynamic information sharing environments
The quality of information is crucial for decision making in many mission-critical applications such as battlefield operations and intelligence analysis. However, as the system becomes larger and more diverse, it is becoming increasingly difficult to assess the quality of information from various operators or data sources. In this paper we propose an agent-based approach to managing the quality of information, e.g., its trustworthiness, in network centric information sharing environments, where software agents collaborate with each other to automatically represent and assess the trustworthiness of information from its pedigree within the framework of Dempster-Shafer theory.
14866925
A new edge detector based on Fresnel diffraction
This paper proposed an edge detection scheme which is deduced from Fresnel diffraction. Analysis in this paper shows that Fresnel convolution kernel function performs well on edge enhancement when images are transformed into complex functions. Due to its mathematical complexity, the method is simplified into a linear convolution filter. The new edge detector is designed based on the simplified linear filter. Experimental results indicate that the new detector gives quantitative results equal to the Canny detector while it is more simple to be implemented.