Related papers: Data analysis recipes: Fitting a model to data
We consider the fitting of heavy tailed data and distribution with a special attention to distributions with a non--standard shape in the "body" of the distribution. To this end we consider a dense class of heavy tailed distributions…
Data-driven modeling is useful for reconstructing nonlinear dynamical systems when the underlying process is unknown or too expensive to compute. Having reliable uncertainty assessment of the forecast enables tools to be deployed to predict…
Probabilistic models analyze data by relying on a set of assumptions. Data that exhibit deviations from these assumptions can undermine inference and prediction quality. Robust models offer protection against mismatch between a model's…
We extend conformal prediction methodology beyond the case of exchangeable data. In particular, we show that a weighted version of conformal prediction can be used to compute distribution-free prediction intervals for problems in which the…
In scientific inference problems, the underlying statistical modeling assumptions have a crucial impact on the end results. There exist, however, only a few automatic means for validating these fundamental modelling assumptions. The…
This work introduces a method for fitting to the degree distributions of complex network datasets, such that the most appropriate distribution from a set of candidate distributions is chosen while maximizing the portion of the distribution…
It is now practically the norm for data to be very high dimensional in areas such as genetics, machine vision, image analysis and many others. When analyzing such data, parametric models are often too inflexible while nonparametric…
We describe an approach to improving model fitting and model generalization that considers the entropy of distributions of modelling residuals. We use simple simulations to demonstrate the observational signatures of overfitting on ordered…
Aggregated Relational Data (ARD) contain summary information about individual social networks and are widely used to estimate social network characteristics and the size of populations of interest. Although a variety of ARD estimators…
The problem of fitting experimental data to a given model function $f(t; p_1,p_2,\dots,p_N)$ is conventionally solved numerically by methods such as that of Levenberg-Marquardt, which are based on approximating the Chi-squared measure of…
This paper develops a methodology for approximating the posterior first two moments of the posterior distribution in Bayesian inference. Partially specified probability models, which are defined only by specifying means and variances, are…
Data-driven methods for modeling dynamic systems have received considerable attention as they provide a mechanism for control synthesis directly from the observed time-series data. In the absence of prior assumptions on how the time-series…
Generalized linear models (GLMs) are popular for data-analysis in almost all quantitative sciences, but the choice of likelihood family and link function is often difficult. This motivates the search for likelihoods and links that minimize…
Despite the progress in the development of generative models, their usefulness in creating synthetic data that improve prediction performance of classifiers has been put into question. Besides heuristic principles such as "synthetic data…
This paper presents a comprehensive algorithm for fitting generative models whose likelihood, moments, and other quantities typically used for inference are not analytically or numerically tractable. The proposed method aims to provide a…
Linear models are foundational tools in statistics and ubiquitous across the applied sciences. However, conventional statistical inference -- such as $t$-tests and $F$-tests -- are only valid at fixed sample sizes, making them unsuitable…
Traditionally regression analysis answers questions about the relationships among variables based on the assumption that the observation values of variables are precise numbers. It has long been dominated by least squares techniques, mostly…
Given a family of pretrained models and a hold-out set, how can we construct a valid conformal prediction set while selecting a model that minimizes the width of the set? If we use the same hold-out data set both to select a model (the…
Motivated by two case studies using primary care records from the Clinical Practice Research Datalink, we describe statistical methods that facilitate the analysis of tall data, with very large numbers of observations. Our focus is on…
Many applications of machine learning methods involve an iterative protocol in which data are collected, a model is trained, and then outputs of that model are used to choose what data to consider next. For example, one data-driven approach…