the helmholtz machine discovering the structure inherent in a set of patterns is a fundamental aim of statistical inference or learning one fruitful approach is to build a parameterized stochastic generative model independent draws from which are likely to produce the patterns for all but the simplest generative models each pattern can be generated in exponentially many ways it is thus intractable to adjust the parameters to maximize the probability of the observed patterns we describe a way of finessing this combinatorial explosion by maximizing an easily computed lower bound on the probability of the observations our method can be viewed as a form of hierarchical self supervised learning that may relate to the function of bottom up and top down cortical processing pathways

advances on byy harmony learning information theoretic perspective generalized projection geometry and independent factor autodetermination the nature of bayesian ying yang harmony learning is reexamined from an information theoretic perspective not only its ability for model selection and regularization is explained with new insights but also discussions are made on its relations and differences from the studies of minimum description length mdl bayesian approach the bit back based mdl akaike information criterion aic maximum likelihood information geometry helmholtz machines and variational approximation moreover a generalized projection geometry is introduced for further understanding such a new mechanism furthermore new algorithms are also developed for implementing gaussian factor analysis fa and non gaussian factor analysis nfa such that selecting appropriate factors is automatically made during parameter learning

model selection and akaike s information criterion aic the general theory and its analytical extensions during the last fifteen years akaike s entropy based information criterion aic has had a fundamental impact in statistical model evaluation problems this paper studies the general theory of the aic procedure and provides its analytical extensions in two ways without violating akaike s main principles these extensions make aic asymptotically consistent and penalize overparameterization more stringently to pick only the simplest of the true models these selection criteria are called caic and caicf asymptotic properties of aic and its extensions are investigated and empirical performances of these criteria are studied in choosing the correct degree of a polynomial model in two different monte carlo experiments under different conditions

local error estimates for some petrov galerkin methods applied to strongly elliptic equations on curves on etudie les proprietes de convergence locales de quelques methodes de petrov galerkin appliquees aux equations fortement elliptiques sur des courbes regulieres du plan on etablit des estimations d erreurs locales pour une grande echelle de normes de sobolev

mesh grading for integral equations of the first kind with logarithmic kernel when the galerkin method is used to solve the first kind integral equations with logarithmic kernel on polygons or open arcs the singularities of the solution degrade the rates of convergence the aim of this paper is to show for the particular case of piecewise constant approximation spaces that in some cases the o h 3 order of convergence can be restored by a suitable grading of the mesh

on the numerical solution of a logarithmic integral equation of the first kind for the helmholtz equation we describe a quadrature method for the numerical solution of the logarithmic integral equation of the first kind arising from the single layer approach to the dirichlet problem for the two dimensional helmholtz equation in smooth domains we develop an error analysis in a sobolev space setting and prove fast convergence rates for smooth boundary data

universally catenarian integral domains abstract the rings of the title are the not necessarily noetherian integral domains r such that r x 1 x n is catenarian for each positive integer n it is proved that each such r must be a stably strong s domain in the sense of malik mott the class of all universally catenarian integral domains is characterized as the largest class of catenarian integral domains which is stable under factor domains and localizations and whose members r satisfy the altitude formula and dim v r dim r moreover the following theorem is given generalizing ratliff s result that each one dimensional noetherian integral domain is universally catenarian let r be a locally finite dimensional going down domain then r is universally catenarian if and only if the integral closure of r is a prufer domain other results and applications are also given

numerically pricing convertible bonds under stochastic volatility or stochastic interest rate with an adi based predictor corrector scheme abstract in this paper the pricing problem for the american style convertible bonds with the heston stochastic volatility and that with the cox ingersoll ross cir stochastic interest rate are both considered due to the complexity of both problems resulting from an additional stochastic factor it is almost impossible to find any analytical solution therefore a predictor corrector scheme is chosen as the numerical scheme to solve the partial differential equations pdes with the douglas rachford d r method being utilized as one of the alternating direction implicit adi methods for the correction step to obtain the numerical solution finally the accuracy of our approach is numerically verified and different properties of convertible bond price and the optimal conversion price are also demonstrated and discussed through examples

stochastic complexity and modeling on demontre un theoreme fondamental qui donne une borne inferieure pour la longueur de code et donc pour les erreurs de prediction on definit les notions d information a priori et d information utile dans les donnees

on questions related to stably strong s domains abstract the main purpose of this paper is to study when a t i d construction ring is a stably strong s ring this allows us to generalize and improve some known results and to discover new classes of stably strong s domains we propose a positive answer in a special case of this construction to the famous problem is r stably strong s when r x is strong s

temporal byy encoding markovian state spaces and space dimension determination as a complementary to those temporal coding approaches of the current major stream this paper aims at the markovian state space temporal models from the perspective of the temporal bayesian ying yang byy learning with both new insights and new results on not only the discrete state featured hidden markov model and extensions but also the continuous state featured linear state spaces and extensions especially with a new learning mechanism that makes selection of the state number or the dimension of state space either automatically during adaptive learning or subsequently after learning via model selection criteria obtained from this mechanism experiments are demonstrated to show how the proposed approach works

local error estimates for the galerkin method applied to strongly elliptic integral equations on open curves saranen math comp 48 1987 pp 485 502 proved local estimates in sobolev norms for the galerkin method applied to strongly elliptic equations on smooth closed curves in the plane we extend his results to the case of open curves of particular interest are weakly singular and hypersingular integral equations on a slit an interesting outcome from our result is that we can judge the orders of convergence of the local errors in some norms that do not exist in the global sense

a predictor corrector scheme based on the adi method for pricing american puts with stochastic volatility abstract in this paper we introduce a new numerical scheme based on the adi alternating direction implicit method to price american put options with a stochastic volatility model upon applying a front fixing transformation to transform the unknown free boundary into a known and fixed boundary in the transformed space a predictor corrector finite difference scheme is then developed to solve for the optimal exercise price and the option values simultaneously based on the local von neumann stability analysis a stability requirement is theoretically obtained first and then tested numerically it is shown that the instability introduced by the predictor can be damped to some extent by the adi method that is used in the corrector the results of various numerical experiments show that this new approach is fast and accurate and can be easily extended to other types of financial derivatives with an american style exercise another key contribution of this paper is the proposition of a set of appropriate boundary conditions particularly in the volatility direction upon realizing that appropriate boundary conditions in the volatility direction for stochastic volatility models appear to be controversial in the literature a sound justification is also provided for the proposed boundary conditions mathematically as well as financially

the k operator and the galerkin method for strongly elliptic equations on smooth curves local estimates superconvergence in the l2 norm for the galerkin approximation of the integral equation lu f is studied where i is a strongly elliptic pseudodifferential operator on a smooth closed or open curve let uf be the galerkin approximation to u by using the operator an operator that averages the values of uh we will construct a better approximation than uh itself that better approximation is a legacy of the highest order of convergence in negative norms for symm s equation on a slit the same order of convergence can be recovered if the mesh is suitably graded in this paper we shall study a way of increasing the order of local convergence in the l2 norm for the galerkin approximation to the solution of strongly ellip tic pseudodifferential equations on a smooth closed or open curve in r2 this kind of integral equation is of importance in solving interior or exterior bound ary value problems of potential theory the most common example is symm s first kind integral equation with logarithmic kernel see 6 7 12 other appli cations are hypersingular integral equations and singular integral equations of cauchy type which occur e g in elasticity see 18 for general petrov galerkin methods when smoothest splines are used as trial and test functions local error estimates were proved in 11 for smooth closed curves and in 16 for smooth open curves consider for example symm s equation with piecewise constant functions used as trial and test functions it was proved that the local l2 error converges with order 0 h in the case of smooth closed curves 11 and with order 0 hxi2 in the case of smooth open curves 16 however it is well known that the highest orders of global convergence achieved in negative norms are 0 h3 for the closed smooth case 5 and 0 h for the open smooth case 4 13 the purpose of this article is to construct from the galerkin solution a better approximate solution which inherits the highest possible orders of global convergence to give best local con vergence in the l2 norm e g in the example mentioned above order 0 hy for the closed case and 0 h for the open case can be achieved locally in the l2 norm that better approximation is constructed by averaging the values of the galerkin solution using the k operator

sur les s domaines forts de kaplansky abstract in this paper we deal with the study of the stably strong s domain property for pull back constructions some applications are given in section 1 the main purpose of section 2 is to construct a new example of stably strong s domains

coupling of finite element and boundary integral methods for electromagnetic scattering in a two layered medium consider a time harmonic electromagnetic plane wave incident on an inhomogeneity embedded in a two layered medium in this paper a method of coupling of finite element and boundary integral equation methods is presented for the solutions of electromagnetic scattering in both transverse electric and magnetic polarization cases the well posedness of the continuous and discrete problems as well as optimal error estimates for the coupled variational approximations are obtained numerical results are included to illustrate the accuracy with the optimal convergence property of the proposed method and to show the wave features in a two layered medium

temporal byy learning for state space approach hidden markov model and blind source separation the temporal bayesian yang yang tbyy learning has been presented for signal modeling in a general state space approach which provides not only a unified point of view on the kalman filter hidden markov model hmm independent component analysis ica and blind source separation bss with extensions but also further advances on these studies including a higher order hmm independent hmm for binary bss temporal ica tica and temporal factor analysis for real bss without and with noise adaptive algorithms are developed for implementation and criteria are provided for selecting an appropriate number of states or sources moreover theorems are given on the conditions for source separation by linear and nonlinear tica particularly it has been shown that not only non gaussian but also gaussian sources can also be separated by tica via exploring temporal dependence experiments are also demonstrated

duality estimates for the numerical solution of integral equations we formulate and prove aubin nitsche type duality estimates for the error of general projection methods examples of applications include collocation methods and augmented galerkin methods for boundary integral equations on plane domains with corners and three dimensional screen and crack problems for some of these methods we obtain higher order error estimates in negative norms in cases where previous formulations of the duality arguments were not applicable

stock loan valuation under a stochastic interest rate model stock loans are loans collateralized by stocks they are modern financial products designed for investors with large equity positions mathematically stock loans can be regarded as american call options with a time dependent strike price this study is the first in the literature that considers the valuation of stock loans in a stochastic interest rate framework based on portfolio analysis a partial differential equation pde governing the value of stock loans is derived a set of appropriate boundary conditions particularly in the interest rate direction are also proposed to close the pricing system a sound justification is provided for the proposed boundary conditions mathematically as well as financially to solve the proposed nonlinear pde system a predictor corrector finite difference method is adopted moreover an alternating direction implicit adi method is used to improve the computational efficiency numerical results suggest that the current method is reliable and the stochastic interest rate leads to a higher optimal exercise price of the stock loan in comparison with that calculated from the black scholes model

a new predictor corrector scheme for valuing american puts abstract in this paper we present a new numerical scheme based on the finite difference method to solve american put option pricing problems upon applying a landau transform or the so called front fixing technique 19 to the black scholes partial differential equation a predictor corrector finite difference scheme is proposed to numerically solve the nonlinear differential system through the comparison with zhu s analytical solution 35 we shall demonstrate that the numerical results obtained from the new scheme converge well to the exact optimal exercise boundary and option values the results of our numerical examples suggest that this approach can be used as an accurate and efficient method even for pricing other types of financial derivative with american style exercise

byy harmony learning independent state space and generalized apt financial analyses first the relationship between factor analysis fa and the well known arbitrage pricing theory apt for financial market is discussed comparatively with a number of to be improved problems listed an overview is made from a unified perspective on the related studies in the literatures of statistics control theory signal processing and neural networks next we introduce the fundamentals of the bayesian ying yang byy system and the harmony learning principle we further show that a specific case of the framework called byy independent state space iss system provides a general guide for systematically tackling various fa related learning tasks and the above to be improved problems for the apt analyses third on various specific cases of the byy iss system in three typical architectures adaptive algorithms regularization methods and model selection criteria are provided for either or both of parameter learning with automated model selection and parameter learning followed by model selection finally we introduce some other financial applications that are based on the underlying independent factors via the apt analyses

a penalty method for american options with jump diffusion processes the fair price for an american option where the underlying asset follows a jump diffusion process can be formulated as a partial integral differential linear complementarity problem we develop an implicit discretization method for pricing such american options the jump diffusion correlation integral term is computed using an iterative method coupled with an fft while the american constraint is imposed by using a penalty method we derive sufficient conditions for global convergence of the discrete penalized equations at each timestep finally we present numerical tests which illustrate such convergence

a unified perspective and new results on rht computing mixture based learning and multi learner based problem solving on one hand multiple object detection approaches of hough transform ht type and randomized ht type have been extended into an evidence accumulation featured general framework for problem solving with five key mechanisms elaborated and several extensions of ht and rht presented on the other hand another framework is proposed to integrate typical multi learner based approaches for problem solving particularly on gaussian mixture based data clustering and local subspace learning multi sets mixture based object detection and motion estimation and multi agent coordinated problem solving typical learning algorithms especially those that base on rival penalized competitive learning rpcl and bayesian ying yang byy learning are summarized from a unified perspective with new extensions furthermore the two different frameworks are not only examined with one viewed crossly from a perspective of the other with new insights and extensions but also further unified into a general problem solving paradigm that consists of five basic mechanisms in terms of acquisition allocation amalgamation admission and affirmation or shortly a5 paradigm