Non-linear estimation is easy

Non-linear state estimation and some related topics, like parametric estimation, fault diagnosis, and perturbation attenuation, are tackled here via a new methodology in numerical differentiation. The corresponding basic system theoretic definitions and properties are presented within the framework of differential algebra, which permits to handle system variables and their derivatives of any order. Several academic examples and their computer simulations, with on-line estimations, are illustrating our viewpoint

Quantum Circulant Preconditioner for Linear System of Equations

We consider the quantum linear solver for $Ax=b$ with the circulant preconditioner $C$. The main technique is the singular value estimation (SVE) introduced in [I. Kerenidis and A. Prakash, Quantum recommendation system, in ITCS 2017]. However, some modifications of SVE should be made to solve the preconditioned linear system $C^{-1} Ax = C^{-1} b$. Moreover, different from the preconditioned linear system considered in [B. D. Clader, B. C. Jacobs, C. R. Sprouse, Preconditioned quantum linear system algorithm, Phys. Rev. Lett., 2013], the circulant preconditioner is easy to construct and can be directly applied to general dense non-Hermitian cases. The time complexity depends on the condition numbers of $C$ and $C^{-1} A$, as well as the Frobenius norm $\|A\|_F$

Structured variable selection and estimation

In linear regression problems with related predictors, it is desirable to do variable selection and estimation by maintaining the hierarchical or structural relationships among predictors. In this paper we propose non-negative garrote methods that can naturally incorporate such relationships defined through effect heredity principles or marginality principles. We show that the methods are very easy to compute and enjoy nice theoretical properties. We also show that the methods can be easily extended to deal with more general regression problems such as generalized linear models. Simulations and real examples are used to illustrate the merits of the proposed methods.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS254 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

On Marginal and Interaction Effects: The Case of Heckit and Two-Part Models

Interaction effects capture the impact of one explanatory variable x1 on the marginal effect of another explanatory variable x2. To explore interaction effects, so-called interaction terms x1x2 are typically included in estimation specifications. While in linear models the effect of a marginal change in the interaction term is equal to the interaction effect, this equality generally does not hold in non-linear specifications (AI, NORTON, 2003). This paper provides for a general derivation of marginal and interaction effects in both linear and non-linear models and calculates the formulae of the marginal and interaction effects resulting from HECKMAN's sample selection model as well as the Two-Part Model, two commonly employed censored regression models. Drawing on a survey of automobile use from Germany, we argue that while it is important to test for the significance of interaction effects, their size conveys limited substantive content. More meaningful, and also more easy to grasp, are the conditional marginal effects pertaining to two variables that are assumed to interact.Censored regression models, interaction terms

Estimation of elastic and viscous properties of the left ventricle based on annulus plane harmonic behavior

Assessment of left ventricular (LV) function with an emphasis on contractility has been a challenge in cardiac mechanics during the recent decades. The LV function is usually described by the LV pressurevolume (P-V) diagram. The standard P-V diagrams are easy to interpret but difficult to obtain and require invasive instrumentation for measuring the corresponding volume and pressure data. In the present study, we introduce a technique that can estimate the viscoelastic properties of the LV based on harmonic behavior of the ventricular chamber and it can be applied non-invasively as well. The estimation technique is based on modeling the actual long axis displacement of the mitral annulus plane toward the cardiac base as a linear damped oscillator with time-varying coefficients. The time-varying parameters of the model were estimated by a standard Recursive Linear Least Squares (RLLS) technique. LV stiffness at end-systole and end diastole was in the range of 61.86-136.00 dyne/g.cm and 1.25-21.02 dyne/g.cm, respectively. The only input used in this model was the long axis displacement of the annulus plane, which can also be obtained non-invasively using tissue Doppler or MR imaging

NICE: Non-linear Independent Components Estimation

We propose a deep learning framework for modeling complex high-dimensional densities called Non-linear Independent Component Estimation (NICE). It is based on the idea that a good representation is one in which the data has a distribution that is easy to model. For this purpose, a non-linear deterministic transformation of the data is learned that maps it to a latent space so as to make the transformed data conform to a factorized distribution, i.e., resulting in independent latent variables. We parametrize this transformation so that computing the Jacobian determinant and inverse transform is trivial, yet we maintain the ability to learn complex non-linear transformations, via a composition of simple building blocks, each based on a deep neural network. The training criterion is simply the exact log-likelihood, which is tractable. Unbiased ancestral sampling is also easy. We show that this approach yields good generative models on four image datasets and can be used for inpainting.Comment: 11 pages and 2 pages Appendix, workshop paper at ICLR 201

Estimation of algal growth parameters from vertical primary production profiles

Phytoplankton maximum growth rate and the saturation light intensity, Is, can be estimated from vertical profiles of primary production by non-linear least-squares estimation. Solution through the normal equations leads to formulae which are relatively simple and easy to implement. The computation of confidence contours is demonstrated, and the results are contrasted to the confidence limits on the parameters individually. These can be quite misleading due to model non-linearity and correlation between parameter estimation.\ud \ud The procedure has been applied to primary production data from Lake Balaton, a shallow lake in Hungary. The growth rate-temperature relation is analysed by separating the parameters into two groups characteristic for “warm” and “cold” water phytoplankton, respectively. A bell-shaped curve is found for “cold” water communities, with an optimum at about 7–9°C, whereas the “warm” water phytoplankton exhibits a strong exponential dependency in the temperature range of interest (up to 25°C). Is also appears to be related to temperature except for the “cold” water group, where Is is essentially constant. However, a roughly linear relation with considerably less scatter is obtained when Is is plotted directly versus day-averaged solar radiation. This apparent fast adaptation is attributed to the extremely short turnover time in Lake Balaton. Maximum growth rates of 10–20 d−1 have been found for temperatures between 20 and 25°C. These results and a critical appraisal of available literature suggest that the common notion of maximum growth rates being in the order of 1–3 d−1 needs revision, at least for lakes with relatively high summer temperatures

Forecasting exchange rates of major currencies with long maturity forward rates. Bruegel Working Paper | Issue 02 April 2020. Plus Annex in separate pdf

This paper presents unprecedented exchange rate forecasting results, based upon a new model that approximates the gap between the fundamental equilibrium exchange rate and the actual exchange rate with the longmaturity forward exchange rate. The theoretical derivation of our forecasting equation is consistent with the monetary model of exchange rates. Our model outperforms the random walk in out-of-sample forecasting of twelve major currency pairs over the short and long horizon forecasts for the 1990- 2020 period. The results are robust for all sub-periods, with the exception of the years around the collapse of Lehman Brothers in September 2008. Our results are robust to alternative model specifications, single equation and panel estimation, recursive and rolling estimation, and alternate data construction methods. The model performs better when the long-maturity forward exchange rate is assumed to be stationary, as opposed to assuming non-stationarity. The improvement in forecast accuracy from our model is economically and statistically significant for almost all exchange-rate series. The model is simple, linear, easy to replicate, and the data we use is available in real time and not subject to revision