Related papers: Effective Degrees of Freedom: A Flawed Metaphor
A model-free measure of coupling between dynamical variables is built from time series embedding principle. The approach described does not require a mathematical form for the dynamics to be assumed. The approach also does not require…
Interpretation methods to reveal the internal reasoning processes behind machine learning models have attracted increasing attention in recent years. To quantify the extent to which the identified interpretations truly reflect the intrinsic…
We propose a decision-analytical approach to comparing the flexibility of decision situations from the perspective of a decision-maker who exhibits constant risk-aversion over a monetary value model. Our approach is simple yet seems to be…
We consider high-dimensional estimation problems where the number of parameters diverges with the sample size. General conditions are established for consistency, uniqueness, and asymptotic normality in both unpenalized and penalized…
In this letter, we describe a very general procedure to obtain a causal fit of the permittivity of materials from experimental data with very few parameters. Unlike other closed forms proposed in the literature, the particularity of this…
This contribution to the debate on confidence limits focuses mostly on the case of measurements with `open likelihood', in the sense that it is defined in the text. I will show that, though a prior-free assessment of {\it confidence} is, in…
Many widely used models amount to an elaborate means of making up numbers--but once a number has been produced, it tends to be taken seriously and its source (the model) is rarely examined carefully. Many widely used models have little…
Empirical process theory for i.i.d. observations has emerged as a ubiquitous tool for understanding the generalization properties of various statistical problems. However, in many applications where the data exhibit temporal dependencies…
High-dimensional Bayesian procedures often exhibit behavior that is effectively low dimensional, even when the ambient parameter space is large or infinite-dimensional. This phenomenon underlies the success of shrinkage priors,…
The algebra of linear and quadratic functions of basic observables on the phase space of either the free particle or the harmonic oscillator possesses a finite-dimensional anomaly. The quantization of these systems outside the critical…
In this paper, we investigate the degrees of freedom ($\dof$) of penalized $\ell_1$ minimization (also known as the Lasso) for linear regression models. We give a closed-form expression of the $\dof$ of the Lasso response. Namely, we show…
The term "researcher degrees of freedom" (RDF), which was introduced in metascientific literature in the context of the replication crisis in science, refers to the extent of flexibility a scientist has in making decisions related to data…
We classify (up to quasi-isomorphism) the free differential modules whose homology is equal to a given module $M$ by developing a theory for deforming an arbitrary free complex into a differential module. We use an iterative approach to…
For the last two decades, high-dimensional data and methods have proliferated throughout the literature. Yet, the classical technique of linear regression has not lost its usefulness in applications. In fact, many high-dimensional…
For physical theories, the degree of arbitrariness of a system is of great importance, and is often closely linked to the concept of degree of freedom, and for most systems this number is far from obvious. In this paper we present an easy…
Systems design processes are increasingly reliant on simulation models to inform design decisions. A pervasive issue within the systems engineering community is trusting in the models used to make decisions about complex systems. This work…
Perplexity -- a function measuring a model's overall level of "surprise" when encountering a particular output -- has gained significant traction in recent years, both as a loss function and as a simple-to-compute metric of model quality.…
Model complexity is an important factor to consider when selecting among graphical models. When all variables are observed, the complexity of a model can be measured by its standard dimension, i.e. the number of independent parameters. When…
Functions of one or more variables are usually approximated with a basis: a complete, linearly-independent system of functions that spans a suitable function space. The topic of this paper is the numerical approximation of functions using…
The quest for a formula that satisfactorily measures the effective degrees of freedom in kernel density estimation (KDE) is a long standing problem with few solutions. Starting from the orthogonal polynomial sequence (OPS) expansion for the…