Parameter Learning of Logic Programs for Symbolic-Statistical Modeling

We propose a logical/mathematical framework for statistical parameter learning of parameterized logic programs, i.e. definite clause programs containing probabilistic facts with a parameterized distribution. It extends the traditional least Herbrand model semantics in logic programming to distribution semantics, possible world semantics with a probability distribution which is unconditionally applicable to arbitrary logic programs including ones for HMMs, PCFGs and Bayesian networks. We also propose a new EM algorithm, the graphical EM algorithm, that runs for a class of parameterized logic programs representing sequential decision processes where each decision is exclusive and independent. It runs on a new data structure called support graphs describing the logical relationship between observations and their explanations, and learns parameters by computing inside and outside probability generalized for logic programs. The complexity analysis shows that when combined with OLDT search for all explanations for observations, the graphical EM algorithm, despite its generality, has the same time complexity as existing EM algorithms, i.e. the Baum-Welch algorithm for HMMs, the Inside-Outside algorithm for PCFGs, and the one for singly connected Bayesian networks that have been developed independently in each research field. Learning experiments with PCFGs using two corpora of moderate size indicate that the graphical EM algorithm can significantly outperform the Inside-Outside algorithm

Circumnuclear molecular gas in starburst and Seyfert galaxies

In order to investigate circumnuclear molecular gaseous contents and their relation to the nuclear activity, researchers made a search for circumnuclear (12)CO (J=1-0) emission from 28 starburst-nucleus galaxies (SBNs) and 12 Seyfert galaxies with the recession velocities less than 5000 km/s, using the Nobeyama Radio Observatory 45-m telescope. The full half-power beam width of 17 arcsec covers a region of less than about 5 kpc in diameter for the sample galaxies. The circumnuclear CO emission was detected from twelve SBNs (one is marginal) and four Seyfert galaxies. The main results and conclusions are summarized. Researchers derived the circumnuclear surface density of molecular gas which is corrected for inclination of the galaxies. This analysis shows that the surface density spans a wide range over two orders of magnitude. Further, there is no significant difference in the surface densities between types 1 and 2 Seyfert galaxies. Thus, we may conclude that the circumnuclear molecular content is not a key parameter producing the dichotomy of the Seyfert galaxies. It is also shown that there is no significant difference in the circumnuclear surface densities of molecular gas among the Seyfert, starburst, and normal galaxies. This implies that the circumnuclear gaseous content is not a key parameter determining which activity occurs in nuclei. We may conclude that more centrally condensed (i.e., less than 10 - 100 pc in diameter) gas components play an essential role on the occurrence of nuclear activities. Comparing results with the previous ones, researchers deduced radial distribution of surface density of molecular gases. They cannot obtain evidence for strong central concentration of molecular gas in the sample Seyfert galaxies except for NGC 3227. This is consistent with the previous result by Blitz, Mathieu, and Bally (1986). Comparing the CO emission line profiles with the previous ones taken with the larger beams, researchers discovered circumnuclear components of molecular gases. In particular, they found that molecular gas clouds may be absent in the SE of the nucleus of NGC 7469 where the high-excitation emitting region is discovered by Heckman et al. (1986). It is suggested that the nuclear activity (strong radiation and/or wind) may destruct the molecular clouds in that region

CHR(PRISM)-based Probabilistic Logic Learning

PRISM is an extension of Prolog with probabilistic predicates and built-in support for expectation-maximization learning. Constraint Handling Rules (CHR) is a high-level programming language based on multi-headed multiset rewrite rules. In this paper, we introduce a new probabilistic logic formalism, called CHRiSM, based on a combination of CHR and PRISM. It can be used for high-level rapid prototyping of complex statistical models by means of "chance rules". The underlying PRISM system can then be used for several probabilistic inference tasks, including probability computation and parameter learning. We define the CHRiSM language in terms of syntax and operational semantics, and illustrate it with examples. We define the notion of ambiguous programs and define a distribution semantics for unambiguous programs. Next, we describe an implementation of CHRiSM, based on CHR(PRISM). We discuss the relation between CHRiSM and other probabilistic logic programming languages, in particular PCHR. Finally we identify potential application domains

A smooth, efficient representation of reflectance

Reflectance plays an important role in computer graphics. It describes the appearance of an object with two directional parameters. Reflectance is critical, because it determines the appearance of the object to be synthesized. Reflectance can be determined either by an analytical model, or by evaluating a fit to a measured reflectance data set. In general, analytical models are complex and computationally expensive to evaluate and it is difficult to control the parameters of the model to obtain a desired appearance. A popular method of fitting data is by using a basis function expansion. However, this method requires many basis functions to represent the strongly-peaked data and the result is computationally expensive. We propose a method to overcome this problem by using a modified N-dimensional multilevel B-spline approximation. Our method fits various reflectance data very well. Multilevel architecture makes it possible to control the accuracy of the fit. A higher level fit uses a denser control mesh and fits more accurately. In addition, the resulting fit is very smooth and efficient to evaluate. The time complexity of evaluation is a constant regardless of the fit level. A higher level fit requires more storage than a lower level fit. The storage might be a problem on memory intensive applications. To overcome this, we represent a data set with two fits, a diffuse fit and a specular fit and we can successfully compress the storage for finer fit without losing major performance from the original method. In addition, by utilizing minimal perfect hashing, we can retrieve the value of each control point efficiently from compressed table

3-D Kinematics of Water Masers in the W51A Region

We report proper motion measurements of water masers in the massive-star forming region W51A and the analyses of the 3-D kinematics of the masers in three maser clusters of W51A (W51 North, Main, and South). In W~51 North, we found a clear expanding flow that has an expansion velocity of ~70 km/s and indicates deceleration. The originating point of the flow coincides within 0.1 as with a silicon-monoxide maser source near the HII region W~51d. In W51 Main, no systematic motion was found in the whole velocity range (158 km/s =< V(lsr) =< -58 km/s) although a stream motion was reported previously in a limited range of the Doppler velocity (54 km/s =< V(lsr) =< 68 kms). Multiple driving sources of outflows are thought to explain the kinematics of W51 Main. In W51 South, an expansion motion like a bipolar flow was marginally visible. Analyses based on diagonalization of the variance-covariance matrix of maser velocity vectors demonstrate that the maser kinematics in W51 North and Main are significantly tri-axially asymmetric. We estimated a distance to W51 North to be 6.1 +/- 1.3 kpc on the basis of the model fitting method adopting a radially expanding flow.Comment: 20 pages, 8 figures, 8 tables, appear in the NRO report No. 564 (ftp://ftp.nro.nao.ac.jp/nroreport/PASJ-W51.pdf) and will appear in Publ. Astron. Soc. Japan, Vol. 54, No. 5 (10/25 issue

Variational Bayes via Propositionalization

We propose a unified approach to VB (variational Bayes) in symbolic-statistical modeling via propositionalization. By propositionalization we mean, broadly, expressing and computing probabilistic models such as BNs (Bayesian networks) and PCFGs (probabilistic context free grammars) in terms of propositional logic that considers propositional variables as binary random variables. Our proposal is motivated by three observations. The first one is that PPC (propostionalized probability computation), i.e. probability computation formalized in a propositional setting, has turned out to be general and efficient when variable values are sparsely interdependent. Examples include (discrete) BNs, PCFGs and more generally PRISM which is a Turing complete logic programming language with EM learning ability we have been developing, and computes probabilities using graphically represented AND/OR boolean formulas. Efficiency of PPC is classically testified by the Inside-Outside algorithm in the case of PCFGs and by recent PPC approaches in the case of BNs such as the one by Darwiche et al. that exploits $0$ probability and CSI (context specific independence). Dechter et al. also revealed that PPC is a general computation scheme for BNs by their formulation of AND/OR search spaces. Second of all, while VB has been around for sometime as a practically effective approach to Bayesian modeling, it\u27s use is still somewhat restricted to simple models such as BNs and HMMs (hidden Markov models) though its usefulness is established through a variety of applications from model selection to prediction. On the other hand it is already proved that VB can be extended to PCFGs and is efficiently implementable using dynamic programming. Note that PCFGs are just one class of PPC and much more general PPC is realized by PRISM. Accordingly if VB is extened to PRISM\u27s PPC, we will obtain VB for general probabilistic models, far wider than BNs and PCFGs. The last observation is that once VB becomes available in PRISM, it saves us a lot of time and energy. First we do not have to derive a new VB algorithm from scratch for each model and implement it. All we have to do is just to write a probabilistic model at predicate level. The rest of work will be carried out automatically in a unified manner by the PRISM system as it happens in the case of EM learning. Deriving and implementing a VB algorithm is a tedious error-prone process, and ensuring its correctness would be difficult beyond PCFGs without formal semantics. PRISM augmented with VB will completely eliminate such needs and make it easy to explore and test new Bayesian models by helping the user cope with data sparseness and avoid over-fitting