We study the distribution of the adaptive LASSO estimator (Zou (2006)) in finite samples as well as in the large-sample limit. The large-sample distributions are derived both for the case where the adaptive LASSO estimator is tuned to perform conservative model selection as well as for the case where the tuning results in consistent model selection. We show that the finite-sample as well as the large-sample distributions are typically highly non-normal, regardless of the choice of the tuning parameter. The uniform convergence rate is also obtained, and is shown to be slower than $n^{-1/2}$ in case the estimator is tuned to perform consistent model selection. In particular, these results question the statistical relevance of the `oracle' property of the adaptive LASSO estimator established in Zou (2006). Moreover, we also provide an impossibility result regarding the estimation of the distribution function of the adaptive LASSO estimator.The theoretical results, which are obtained for a regression model with orthogonal design, are complemented by a Monte Carlo study using non-orthogonal regressors.

Counting and classifying blood cells is an important diagnostic tool in medicine. Support Vector Machines are increasingly popular and efficient and could replace artificial neural network systems. Here a method to classify blood cells is proposed using SVM. A set of statistics on images are implemented in C++. The MPEG-7 descriptors Scalable Color Descriptor, Color Structure Descriptor, Color Layout Descriptor and Homogeneous Texture Descriptor are extended in size and combined with textural features corresponding to textural properties perceived visually by humans. From a set of images of human blood cells these statistics are collected. A SVM is implemented and trained to classify the cell images. The cell images come from a CellaVision DM-96 machine which classify cells from images from microscopy. The output images and classification of the CellaVision machine is taken as ground truth, a truth that is 90-95% correct. The problem is divided in two -- the primary and the simplified. The primary problem is to classify the same classes as the CellaVision machine. The simplified problem is to differ between the five most common types of white blood cells. An encouraging result is achieved in both cases -- error rates of 10.8% and 3.1% -- considering that the SVM is misled by the errors in ground truth. Conclusion is that further investigation of performance is worthwhile.

Motivation: Profile hidden Markov Models (pHMMs) are a popular and very useful tool in the detection of the remote homologue protein families. Unfortunately, their performance is not always satisfactory when proteins are in the 'twilight zone'. We present HMMER-STRUCT, a model construction algorithm and tool that tries to improve pHMM performance by using structural information while training pHMMs. As a first step, HMMER-STRUCT constructs a set of pHMMs. Each pHMM is constructed by weighting each residue in an aligned protein according to a specific structural property of the residue. Properties used were primary, secondary and tertiary structures, accessibility and packing. HMMER-STRUCT then prioritizes the results by voting. Results: We used the SCOP database to perform our experiments. Throughout, we apply leave-one-family-out cross-validation over protein superfamilies. First, we used the MAMMOTH-mult structural aligner to align the training set proteins. Then, we performed two sets of experiments. In a first experiment, we compared structure weighted models against standard pHMMs and against each other. In a second experiment, we compared the voting model against individual pHMMs. We compare method performance through ROC curves and through Precision/Recall curves, and assess significance through the paired two tailed t-test. Our results show significant performance improvements of all structurally weighted models over default HMMER, and a significant improvement in sensitivity of the combined models over both the original model and the structurally weighted models.

We obtain an index of the complexity of a random sequence by allowing the role of the measure in classical probability theory to be played by a function we call the generating mechanism. Typically, this generating mechanism will be a finite automata. We generate a set of biased sequences by applying a finite state automata with a specified number, m, of states to the set of all binary sequences. We detail optimal algorithms to predict sequences generated in this way. We explore a finite setting for the problem of prediction.

Autoencoder neural network is implemented to estimate the missing data. Genetic algorithm is implemented for network optimization and estimating the missing data. Missing data is treated as Missing At Random mechanism by implementing maximum likelihood algorithm. The network performance is determined by calculating the mean square error of the network prediction. The network is further optimized by implementing Decision Forest. The impact of missing data is then investigated and decision forrests are found to improve the results.

Answer set programming (ASP) is a logic programming paradigm that can be used to solve complex combinatorial search problems. Aggregates are an ASP construct that plays an important role in many applications. Defining a satisfactory semantics of aggregates turned out to be a difficult problem, and in this paper we propose a new approach, based on an analogy between aggregates and propositional connectives. First, we extend the definition of an answer set/stable model to cover arbitrary propositional theories; then we define aggregates on top of them both as primitive constructs and as abbreviations for formulas. Our definition of an aggregate combines expressiveness and simplicity, and it inherits many theorems about programs with nested expressions, such as theorems about strong equivalence and splitting.

Counting the number of all the matchings on a bipartite graph has been transformed into calculating the permanent of a matrix obtained from the extended bipartite graph by Yan Huo, and Rasmussen presents a simple approach (RM) to approximate the permanent, which just yields a critical ratio O($n\omega(n)$) for almost all the 0-1 matrices, provided it's a simple promising practical way to compute this #P-complete problem. In this paper, the performance of this method will be shown when it's applied to compute all the matchings based on that transformation. The critical ratio will be proved to be very large with a certain probability, owning an increasing factor larger than any polynomial of $n$ even in the sense for almost all the 0-1 matrices. Hence, RM fails to work well when counting all the matchings via computing the permanent of the matrix. In other words, we must carefully utilize the known methods of estimating the permanent to count all the matchings through that transformation.

This paper proposes a novel solution to spam detection inspired by a model of the adaptive immune system known as the crossregulation model. We report on the testing of a preliminary algorithm on six e-mail corpora. We also compare our results statically and dynamically with those obtained by the Naive Bayes classifier and another binary classification method we developed previously for biomedical text-mining applications. We show that the cross-regulation model is competitive against those and thus promising as a bio-inspired algorithm for spam detection in particular, and binary classification in general.

The paper introduces the notion of off-line justification for Answer Set Programming (ASP). Justifications provide a graph-based explanation of the truth value of an atom w.r.t. a given answer set. The paper extends also this notion to provide justification of atoms during the computation of an answer set (on-line justification), and presents an integration of on-line justifications within the computation model of Smodels. Off-line and on-line justifications provide useful tools to enhance understanding of ASP, and they offer a basic data structure to support methodologies and tools for debugging answer set programs. A preliminary implementation has been developed in ASP-PROLOG. (To appear in Theory and Practice of Logic Programming (TPLP))

To appear in Theory and Practice of Logic Programming (TPLP) This paper develops a declarative language, P-log, that combines logical and probabilistic arguments in its reasoning. Answer Set Prolog is used as the logical foundation, while causal Bayes nets serve as a probabilistic foundation. We give several nontrivial examples and illustrate the use of P-log for knowledge representation and updating of knowledge. We argue that our approach to updates is more appealing than existing approaches. We give sufficiency conditions for the coherency of P-log programs and show that Bayes nets can be easily mapped to coherent P-log programs.