In praise of partially interpretable predictors

Often there is an uninterpretable model that is statistically as good as, if not better than, a successful interpretable model. Accordingly, if one restricts attention to interpretable models, then one may sacrifice predictive power or other desirable properties. A minimal condition for an interpretable, usually parametric, model to be better than another model is that the first should have smallermean-squared error or integratedmean-squared error.We show through a series of examples that this is often not the case and give the asymptotic forms of a variety of interpretable, partially interpretable, and noninterpretable methods. We find techniques that combine aspects of both interpretability and noninterpretability in models seem to give the best results

Extended Kramers-Moyal analysis applied to optical trapping

The Kramers-Moyal analysis is a well established approach to analyze stochastic time series from complex systems. If the sampling interval of a measured time series is too low, systematic errors occur in the analysis results. These errors are labeled as finite time effects in the literature. In the present article, we present some new insights about these effects and discuss the limitations of a previously published method to estimate Kramers-Moyal coefficients at the presence of finite time effects. To increase the reliability of this method and to avoid misinterpretations, we extend it by the computation of error estimates for estimated parameters using a Monte Carlo error propagation technique. Finally, the extended method is applied to a data set of an optical trapping experiment yielding estimations of the forces acting on a Brownian particle trapped by optical tweezers. We find an increased Markov-Einstein time scale of the order of the relaxation time of the process which can be traced back to memory effects caused by the interaction of the particle and the fluid. Above the Markov-Einstein time scale, the process can be very well described by the classical overdamped Markov model for Brownian motion.Comment: 14 pages, 18 figure

Safety surveillance and the estimation of risk in select populations: Flexible methods to control for confounding while targeting marginal comparisons via standardization

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/152565/1/sim8410_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/152565/2/sim8410.pd

Computational exploration of molecular receptive fields in the olfactory bulb reveals a glomerulus-centric chemical map

© The Author(s) 2020. This article is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.Progress in olfactory research is currently hampered by incomplete knowledge about chemical receptive ranges of primary receptors. Moreover, the chemical logic underlying the arrangement of computational units in the olfactory bulb has still not been resolved. We undertook a large-scale approach at characterising molecular receptive ranges (MRRs) of glomeruli in the dorsal olfactory bulb (dOB) innervated by the MOR18-2 olfactory receptor, also known as Olfr78, with human ortholog OR51E2. Guided by an iterative approach that combined biological screening and machine learning, we selected 214 odorants to characterise the response of MOR18-2 and its neighbouring glomeruli. We found that a combination of conventional physico-chemical and vibrational molecular descriptors performed best in predicting glomerular responses using nonlinear Support-Vector Regression. We also discovered several previously unknown odorants activating MOR18-2 glomeruli, and obtained detailed MRRs of MOR18-2 glomeruli and their neighbours. Our results confirm earlier findings that demonstrated tunotopy, that is, glomeruli with similar tuning curves tend to be located in spatial proximity in the dOB. In addition, our results indicate chemotopy, that is, a preference for glomeruli with similar physico-chemical MRR descriptions being located in spatial proximity. Together, these findings suggest the existence of a partial chemical map underlying glomerular arrangement in the dOB. Our methodology that combines machine learning and physiological measurements lights the way towards future high-throughput studies to deorphanise and characterise structure-activity relationships in olfaction.Peer reviewe

Non-linear regression models for Approximate Bayesian Computation

Approximate Bayesian inference on the basis of summary statistics is well-suited to complex problems for which the likelihood is either mathematically or computationally intractable. However the methods that use rejection suffer from the curse of dimensionality when the number of summary statistics is increased. Here we propose a machine-learning approach to the estimation of the posterior density by introducing two innovations. The new method fits a nonlinear conditional heteroscedastic regression of the parameter on the summary statistics, and then adaptively improves estimation using importance sampling. The new algorithm is compared to the state-of-the-art approximate Bayesian methods, and achieves considerable reduction of the computational burden in two examples of inference in statistical genetics and in a queueing model.Comment: 4 figures; version 3 minor changes; to appear in Statistics and Computin

On the Schoenberg Transformations in Data Analysis: Theory and Illustrations

The class of Schoenberg transformations, embedding Euclidean distances into higher dimensional Euclidean spaces, is presented, and derived from theorems on positive definite and conditionally negative definite matrices. Original results on the arc lengths, angles and curvature of the transformations are proposed, and visualized on artificial data sets by classical multidimensional scaling. A simple distance-based discriminant algorithm illustrates the theory, intimately connected to the Gaussian kernels of Machine Learning

A regularity class for the roots of nonnegative functions

We investigate the regularity of the positive roots of a non-negative function of one-variable. A modified H\"older space $\mathcal{F}^\beta$ is introduced such that if $f\in \mathcal{F}^\beta$ then $f^\alpha \in C^{\alpha \beta}$. This provides sufficient conditions to overcome the usual limitation in the square root case ($\alpha = 1/2$) for H\"older functions that $f^{1/2}$ need be no more than $C^1$ in general. We also derive bounds on the wavelet coefficients of $f^\alpha$, which provide a finer understanding of its local regularity.Comment: 12 page

Wavelet penalized likelihood estimation in generalized functional models

The paper deals with generalized functional regression. The aim is to estimate the influence of covariates on observations, drawn from an exponential distribution. The link considered has a semiparametric expression: if we are interested in a functional influence of some covariates, we authorize others to be modeled linearly. We thus consider a generalized partially linear regression model with unknown regression coefficients and an unknown nonparametric function. We present a maximum penalized likelihood procedure to estimate the components of the model introducing penalty based wavelet estimators. Asymptotic rates of the estimates of both the parametric and the nonparametric part of the model are given and quasi-minimax optimality is obtained under usual conditions in literature. We establish in particular that the LASSO penalty leads to an adaptive estimation with respect to the regularity of the estimated function. An algorithm based on backfitting and Fisher-scoring is also proposed for implementation. Simulations are used to illustrate the finite sample behaviour, including a comparison with kernel and splines based methods

Tune in to your emotions: a robust personalized affective music player

The emotional power of music is exploited in a personalized affective music player (AMP) that selects music for mood enhancement. A biosignal approach is used to measure listeners’ personal emotional reactions to their own music as input for affective user models. Regression and kernel density estimation are applied to model the physiological changes the music elicits. Using these models, personalized music selections based on an affective goal state can be made. The AMP was validated in real-world trials over the course of several weeks. Results show that our models can cope with noisy situations and handle large inter-individual differences in the music domain. The AMP augments music listening where its techniques enable automated affect guidance. Our approach provides valuable insights for affective computing and user modeling, for which the AMP is a suitable carrier application