Related papers: Mouse scales
Although regression trees were originally designed for large datasets, they can profitably be used on small datasets as well, including those from replicated or unreplicated complete factorial experiments. We show that in the latter…
Traditional machine learning (ML) algorithms, such as multiple regression, require human analysts to make decisions on how to treat the data. These decisions can make the model building process subjective and difficult to replicate for…
Understanding the interplay between concurrent length scales is a fundamental issue in many problems involving friction between sliding interfaces, from tribology to the study of earthquakes and seismic faults. On the one hand, a…
We present the first steps of a predicative reconstruction of the constructive Bishop-Cheng measure theory. Working in a semi-formal elaboration of Bishop's set theory and invoking the notion of a set-indexed family of subsets (of a given…
Bottom-up saliency, an early human visual processing, behaves like binary classification of interest and null hypothesis. Its discriminant power, mutual information of image features and class distribution, is closely related to saliency…
A new methodological approach for the study of topology for shapes made of arrangements of lines, planes or solids is presented. Topologies for shapes are traditionally built on the classical theory of point-sets. In this paper, topologies…
We consider the problem of characterizing isomorphisms of types, or, equivalently, constructive cardinality of sets, in the simultaneous presence of disjoint unions, Cartesian products, and exponentials. Mostly relying on results about…
A defining property of complex systems is that they have multiscale structure. How does this multiscale structure come about? We argue that within systems there emerges a hierarchy of scales that contribute to a system's causal workings. An…
Additive feature explanations using Shapley values have become popular for providing transparency into the relative importance of each feature to an individual prediction of a machine learning model. While Shapley values provide a unique…
In this article, we develop and investigate a new classifier based on features extracted using spatial depth. Our construction is based on fitting a generalized additive model to the posterior probabilities of the different competing…
The Shapley value is one of the most widely used measures of feature importance partly as it measures a feature's average effect on a model's prediction. We introduce joint Shapley values, which directly extend Shapley's axioms and…
Working under $AD$, we investigate the length of prewellorderings given by the iterates of $\M_{2k+1}$, which is the minimal proper class mouse with $2k+1$ many Woodin cardinals. In particular, we answer some questions from \cite{Hjorth01}…
Causality plays an important role in understanding intelligent behavior, and there is a wealth of literature on mathematical models for causality, most of which is focused on causal graphs. Causal graphs are a powerful tool for a wide range…
We discuss the Poisson structures on Lie groups and propose an explicit construction of the integrable models on their appropriate Poisson submanifolds. The integrals of motion for the SL(N)-series are computed in cluster variables via the…
We consider the performance of a least-squares regression model, as judged by out-of-sample $R^2$. Shapley values give a fair attribution of the performance of a model to its input features, taking into account interdependencies between…
We provide a geometric interpretation to Bayesian inference that allows us to introduce a natural measure of the level of agreement between priors, likelihoods, and posteriors. The starting point for the construction of our geometry is the…
A scaling on some space is a measurable action of the group of positive real numbers. A measure on a measurable space equipped with a scaling is said to be $\alpha$-homogeneous for some nonzero real number $\alpha$ if the mass of any…
Let $\bar{L}_i\lr X_i$ be a holomorphic line bundle over a compact complex manifold for $i=1,2$. Let $S_i$ denote the associated principal circle-bundle with respect to some hermitian inner product on $\bar{L}_i$. We construct complex…
The class of generic structures among those consisting of the measure algebra of a probability space equipped with an automorphism is axiomatizable by positive sentences interpreted using an approximate semantics. The separable generic…
In this article we construct a maximal set of kernels for a multi-parameter linear scale-space that allow us to construct trees for classification and recognition of one-dimensional continuous signals similar the Gaussian linear scale-space…