Bayesian inference and learning in Gaussian process state-space models with Particle MCMC

State-space models are successfully used in many areas of science, engineering and economics to model time series and dynamical systems. We present a fully Bayesian approach to inference and learning (i.e. state estimation and system identification) in nonlinear nonparametric state-space models. We place a Gaussian process prior over the state transition dynamics, resulting in a flexible model able to capture complex dynamical phenomena. To enable efficient inference, we marginalize over the transition dynamics function and, instead, infer directly the joint smoothing distribution using specially tailored Particle Markov Chain Monte Carlo samplers. Once a sample from the smoothing distribution is computed, the state transition predictive distribution can be formulated analytically. Our approach preserves the full nonparametric expressivity of the model and can make use of sparse Gaussian processes to greatly reduce computational complexity.

Effects of intraperitoneal injection of cortisol on nonspecific immune functions of Ctenopharyngodon idella

After grass carps Ctenopharyngodon idellus were injected with cortisol, with (CBC) and without (C) a cocoa butter carrier, the effects of both slowly and rapidly acting exogenous cortisol oil their non-specific immune functions were investigated. On the one hand, after injection with CBC, the cortisol concentration and lysozyme activity in fish serum were enhanced and were sustained at high levels for a long period (30 days). The killing activity in the serum declined with time, and phagocytosis of head kidney macrophages diminished significantly (P < 0.05 or P < 0.01). The leukocrit values in the high dose group (31-8 mg cortisol fish(-1)) increased over time, however, with the maximum average being 5.6% at day 30. The spleen mass index in the high dose group was 0.93 x 10(-3) after 30 days, notably lower (P < 0.05) than that in the control group. In addition, a decrease in resistance to Aeronionas hydrophilo infection in cortisol-treated fish was shown, with the final cumulative mortalities being 54.5 and 66.7% in the low and high dose groups, respectively. On the other hand, there was a decrease in both serum cortisol concentration and lysozyme activity of the experimental fish within 2 weeks after injection with C, where plasma bactericidal activities in the high dose group (31-8 mg cortisol fish(-1)) were remarkably lower (P < 0.01) than those in the control group at each sampling, but were increased slightly over time. The results of which were different from those in the CBC trial. Phagocytic activity of head kidney macrophages and spleen mass index decreased significantly (P < 0.05), while there were increases in leukocrit value and cumulative mortality due to A. hydrophila. The results of which were similar to those in the CBC trial. This study indicated that the injection of cortisol depressed the non-specific immune functions of the grass carp and increased its susceptibility to disease. (c) 2005 The Fisheries Society of the British Isles.

Classification using log Gaussian Cox processes

McCullagh and Yang (2006) suggest a family of classification algorithms based on Cox processes. We further investigate the log Gaussian variant which has a number of appealing properties. Conditioned on the covariates, the distribution over labels is given by a type of conditional Markov random field. In the supervised case, computation of the predictive probability of a single test point scales linearly with the number of training points and the multiclass generalization is straightforward. We show new links between the supervised method and classical nonparametric methods. We give a detailed analysis of the pairwise graph representable Markov random field, which we use to extend the model to semi-supervised learning problems, and propose an inference method based on graph min-cuts. We give the first experimental analysis on supervised and semi-supervised datasets and show good empirical performance.

Predictive entropy search for efficient global optimization of black-box functions

We propose a novel information-theoretic approach for Bayesian optimization called Predictive Entropy Search (PES). At each iteration, PES selects the next evaluation point that maximizes the expected information gained with respect to the global maximum. PES codifies this intractable acquisition function in terms of the expected reduction in the differential entropy of the predictive distribution. This reformulation allows PES to obtain approximations that are both more accurate and efficient than other alternatives such as Entropy Search (ES). Furthermore, PES can easily perform a fully Bayesian treatment of the model hyperparameters while ES cannot. We evaluate PES in both synthetic and real-world applications, including optimization problems in machine learning, finance, biotechnology, and robotics. We show that the increased accuracy of PES leads to significant gains in optimization performance.

Research on the influence of fabrication parameters on the performance of buried ion-exchanged glass waveguides using the variational method

The variational method is proposed to analyze the influence of the fabrication parameters on the performance of buried K+-Na+ ion-exchanged Er3+-Yb3+ ions co-doped glass waveguide. The unknown parameters of the Hermite-Gaussian functions as the trial field distribution are determined based on the scalar variational principle. It is demonstrated that the results calculated in this paper agree with those measured in the experiment. The mode dimensions, the effective refractive index, and the overlap factor as the functions of the fabrication parameters are investigated. These results of the variational analysis are useful for the design and optimization of Er3+-Yb3+ ions co-doped waveguides.

An ultra-low power CMOS random number generator

This paper proposes an ultra-low power CMOS random number generator (RING), which is based on an oscillator-sampling architecture. The noisy oscillator consists of a dual-drain MOS transistor, a noise generator and a voltage control oscillator. The dual-drain MOS transistor can bring extra-noise to the drain current or the output voltage so that the jitter of the oscillator is much larger than the normal oscillator. The frequency division ratio of the high-frequency sampling oscillator and the noisy oscillator is small. The RNG has been fabricated in a 0.35 mu m CMOS process. It can produce good quality bit streams without any post-processing. The bit rate of this RNG could be as high as 100 kbps. It has a typical ultra-low power dissipation of 0.91 mu W. This novel circuit is a promising unit for low power system and communication applications. (c) 2007 Elsevier Ltd. All rights reserved.

Silica-based 64-channel arrayed waveguide gratings with double functions

Silica-based 64-channel arrayed waveguide gratings (AWGs) with double functions and 0.4 nm (50 GHz) channel spacing have been designed and fabricated. On the same component, Gauss and flat-top output response spectra are obtained simultaneously. The test results show that when the insertion loss ranges from 3.5 dB to 6 dB,the crosstalk is better than -34 dB, the 1 dB bandwidth is 0.12 nm, the 3 dB bandwidth is 0,218 nm, and the polarization-dependent loss (PDL) is less than 0.5 dB for Gauss response. When the insertion loss ranges,from 5.8 dB to 7.8 dB, the crosstalk is better than -30 dB, the 1 dB bandwidth is 0.24 nm, the 3 dB bandwidth is 0.33 nm, and the PDL is less than 0.2 dB for flat-top response.

A criterion for local interconvertibility between all-tripartite Gaussian states

We arrive at a necessary and sufficient criterion that can be readily used for interconvertibility between general, all-tripartite Gaussian states under local quantum operation. The derivation involves a systematic reduction that converts the original complex conditions in high-dimensional, 6n x 6n matrix space eventually into 2 x 2 matrix problems.

Conditions for the local manipulation of all bipartite Gaussian states

We provide a general, necessary, and sufficient condition for the possibility of transforming a mixed bipartite Gaussian state with arbitrarily many modes to another one under arbitrary local Gaussian channels, which do not include classical communication. Moreover, by means of this condition we present a necessary criterion that can be used to check the possibility of a state transformation between two mixed Gaussian states. At the same time, we prove that our criterion can be reduced to the Eisert-Plenio criterion when the mode number is chosen as 1 per side.

Conditions for the local manipulation of tripartite Gaussian states

We present the normal form of the covariance matrix for three-mode tripartite Gaussian states. By means of this result, the general form of a necessary and sufficient criterion for the possibility of a state transformation from one tripartite entangled Gaussian state to another with three modes is found. Moreover, we show that the conditions presented include not only inequalities but equalities as well.

practical type checking of functions defined on context-free languages

A type checking method for the functional language LFC is presented. A distinct feature of LFC is that it uses Context-Free (CF) languages as data types to represent compound data structures. This makes LFC a dynamically typed language. To improve efficiency, a practical type checking method is presented, which consists of both static and dynamic type checking. Although the inclusion relation of CF.languages is not decidable,a special subset of the relation is decidable, i.e., the sentential form relation, which can be statically checked.Moreover, most of the expressions in actual LFC programs appear to satisfy this relation according to the statistic data of experiments. So, despite that the static type checking is not complete, it undertakes most of the type checking task. Consequently the run-time efficiency is effectively improved. Another feature of the type checking is that it converts the expressions with implicit structures to structured representation. Structure reconstruction technique is presented.

pattern matching compilation of functions defined in context-free languages

LFC is a functional language based on recursive functions defined in context-free languages. In this paper, a new pattern matching algorithm for LFC is presented, which can represent a sequence of patterns as an integer by an encoding method. It is a rather simple method and produces efficient case-expressions for pattern matching definitions of LFC. The algorithm can also be used for other functional languages, but for nested patterns it may become complicated and further studies are needed.

facilitating formal specification acquisition by using recursive functions on context-free languages

Although formal specification techniques are very useful in software development, the acquisition of formal specifications is a difficult task. This paper presents the formal specification language LFC, which is designed to facilitate the acquisition and validation of formal specifications. LFC uses context-free languages for syntactic aspect and relies on a new kind of recursive functions, i.e. recursive functions on context-free languages, for semantic aspect of specifications. Construction and validation of LFC specifications are machine-aided. The basic ideas behind LFC, the main aspects of LFC, and the use of LFC and illustrative examples are described.