Related papers: Approximation by filter functions
Belief function theory provides a flexible way to combine information provided by different sources. This combination is usually followed by a decision making which can be handled by a range of decision rules. Some rules help to choose the…
Despite significant developments in Proof Theory, surprisingly little attention has been devoted to the concept of proof verifier. In particular, the mathematical community may be interested in studying different types of proof verifiers…
If two probability density functions (PDFs) have values for their first $n$ moments which are quite close to each other (upper bounds of their differences are known), can it be expected that the PDFs themselves are very similar? Shown below…
Feature selection problems arise in a variety of applications, such as microarray analysis, clinical prediction, text categorization, image classification and face recognition, multi-label learning, and classification of internet traffic.…
When classical particle filtering algorithms are used for maximum likelihood parameter estimation in nonlinear state-space models, a key challenge is that estimates of the likelihood function and its derivatives are inherently noisy. The…
We study a family of distance functions on rankings that allow for asymmetric treatments of alternatives and consider the distinct relevance of the top and bottom positions for ordered lists. We provide a full axiomatic characterization of…
This paper presents a general framework for unifying functional interpretations. It is based on families of parameters allowing for different degrees of freedom on the design of the interpretation. In this way we are able to generalise…
By discussing several examples, the theory of generalized functional models is shown to be very natural for modeling some situations of reasoning under uncertainty. A generalized functional model is a pair (f, P) where f is a function…
Function approximation is a generic process in a variety of computational problems, from data interpolation to the solution of differential equations and inverse problems. In this work, a unified approach for such techniques is…
The Gaussian Filter (GF) is one of the most widely used filtering algorithms; instances are the Extended Kalman Filter, the Unscented Kalman Filter and the Divided Difference Filter. GFs represent the belief of the current state by a…
We present a unified framework for quantifying the similarity between representations through the lens of \textit{usable} information, offering a rigorous theoretical and empirical synthesis across three key dimensions. First, addressing…
Ranking functions used in information retrieval are primarily used in the search engines and they are often adopted for various language processing applications. However, features used in the construction of ranking functions should be…
While belief functions may be seen formally as a generalization of probabilistic distributions, the question of the interactions between belief functions and probability is still an issue in practice. This question is difficult, since the…
This paper is concerned with the analysis of the kernel-based algorithm for gain function approximation in the feedback particle filter. The exact gain function is the solution of a Poisson equation involving a probability-weighted…
What should a function that extrapolates beyond known input/output examples look like? This is a tricky question to answer in general, as any function matching the outputs on those examples can in principle be a correct extrapolant. We…
We consider approximation by functions with finite support and characterize its approximation spaces in terms of interpolation spaces and Lorentz spaces.
We regard explanations as a blending of the input sample and the model's output and offer a few definitions that capture various desired properties of the function that generates these explanations. We study the links between these…
We present a novel task that measures how people generalize objects' causal powers based on observing a single (Experiment 1) or a few (Experiment 2) causal interactions between object pairs. We propose a computational modeling framework…
The problem of assessing the value of a candidate is viewed here as a multiple combination problem. On the one hand a candidate can be evaluated according to different criteria, and on the other hand several experts are supposed to assess…
Neural collaborative filtering is the state of art field in the recommender systems area; it provides some models that obtain accurate predictions and recommendations. These models are regression-based, and they just return rating…