Efficient Computation of Reduced Regression Models

Sequential Bayesian computation of logistic regression models

The Extended Kalman Filter (EKF) algorithm for identification of a state space model is shown to be a sensible tool in estimating a Logistic Regression Model sequentially. A Gaussian probability density over the parameters of the Logistic model is propagated on a sample by sample basis. Two other approaches, the Laplace Approximation and the Variational Approximation are compared with the state...

Cheap Computation of Optimal Reduced Models Using Symbolic Computation

Many methods have been proposed for the reduction of single-variable and multi-variable systems having ordinary denominators and those having delays in their numerators and denominators. In this paper, an algorithm for this purpose is proposed that can be easily used by anybody with not too advanced knowledge of mathematics yielding optimal reduced models. This algorithm makes use of the symbol...

Efficient Gradient Computation for Conditional Gaussian Models

Efficient gradient computation for dynamical models

Data assimilation is a fundamental issue that arises across many scales in neuroscience - ranging from the study of single neurons using single electrode recordings to the interaction of thousands of neurons using fMRI. Data assimilation involves inverting a generative model that can not only explain observed data but also generate predictions. Typically, the model is inverted or fitted using c...

Efficient Quantile Regression for Heteroscedastic Models

Quantile regression provides estimates of a range of conditional quantiles. This stands in contrast to traditional regression techniques, which focus on a single conditional mean function. Lee et al. (2012) proposed efficient quantile regression by rounding the sharp corner of the loss. The main modification generally involves an asymmetric l2 adjustment of the loss function around zero. We ext...