Sparse Linear Identifiable Multivariate Modeling

In this paper we consider sparse and identifiable linear latent variable (factor) and linear Bayesian network models for parsimonious analysis of multivariate data. We propose a computationally efficient method for joint parameter and model inference, and model comparison. It consists of a fully Bayesian hierarchy for sparse models using slab and spike priors (two-component delta-function and continuous mixtures), non-Gaussian latent factors and a stochastic search over the ordering of the variables. The framework, which we call SLIM (Sparse Linear Identifiable Multivariate modeling), is validated and bench-marked on artificial and real biological data sets. SLIM is closest in spirit to LiNGAM (Shimizu et al., 2006), but differs substantially in inference, Bayesian network structure learning and model comparison. Experimentally, SLIM performs equally well or better than LiNGAM with comparable computational complexity. We attribute this mainly to the stochastic search strategy used, and to parsimony (sparsity and identifiability), which is an explicit part of the model. We propose two extensions to the basic i.i.d. linear framework: non-linear dependence on observed variables, called SNIM (Sparse Non-linear Identifiable Multivariate modeling) and allowing for correlations between latent variables, called CSLIM (Correlated SLIM), for the temporal and/or spatial data. The source code and scripts are available from http://cogsys.imm.dtu.dk/slim/.Comment: 45 pages, 17 figure

Estimating and Testing an Exponential-Affine Term Structure Model by Nonlinear Filtering

: In general, the interest rate is not directly observable in the financial market. Short term interest rates are quoted in the money market for maturities up to approximately one year, but longer term interest rates are traded only indirectly through the bond market. In this paper the spot interest rate is described by a bivariate stochastic differential equation state space model that gives rise to an exponential-affine term structure model. We propose a new maximum likelihood method for estimating parameters and interest rates in stochastic differential equations from observed coupon-bearing bond prices. The method utilizes continuous-discrete second order nonlinear filtering techniques. As a preliminary analysis the method is applied to a cross-section of time series of Danish government bond prices. Keywords: Nonlinear filtering, quasi maximum likelihood estimation, state space models, stochastic differential equations, term structure modelling. 1 Corresponding author: Phone +45..