Related papers: Revisiting Functional Derivatives in Multi-object …
Accelerated discovery with machine learning (ML) has begun to provide the advances in efficiency needed to overcome the combinatorial challenge of computational materials design. Nevertheless, ML-accelerated discovery both inherits the…
For a real function, automatic differentiation is such a standard algorithm used to efficiently compute its gradient, that it is integrated in various neural network frameworks. However, despite the recent advances in using complex…
Functional programmers have an established tradition of using traversals as a design pattern to work with recursive data structures. The technique is so prolific that a whole host of libraries have been designed to help in the task of…
We study loss functions that measure the accuracy of a prediction based on multiple data points simultaneously. To our knowledge, such loss functions have not been studied before in the area of property elicitation or in machine learning…
The object of this paper is to introduce a new weighted information generating function whose derivative at point 1 gives some well known measures of information. Some properties and particular cases of the proposed generating function have…
The notion of constructible functions in the setting of tame real geometry has been introduced by Cluckers and Dan Miller in their work on parametric integration of globally subanalytic functions. A function on a globally subanalytic set is…
Functional Distributional Semantics is a framework that aims to learn, from text, semantic representations which can be interpreted in terms of truth. Here we make two contributions to this framework. The first is to show how a type of…
This article develops a novel operational semantics for probabilistic control-flow graphs (pCFGs) of probabilistic imperative programs with random assignment and "observe" (or conditioning) statements. The semantics transforms probability…
The known Complex Step Derivative (CSD) method allows easy and accurate differentiation up to machine precision of real analytic functions by evaluating them a small imaginary step next to the real number line. The current paper proposes…
Personalization aims to characterize individual preferences and is widely applied across many fields. However, conventional personalized methods operate in a centralized manner, potentially exposing raw data when pooling individual…
Statistical analysis of functional data is challenging due to their complex patterns, for which functional depth provides an effective means of reflecting their ordering structure. In this work, we investigate practical aspects of the…
There are many possible definitions of derivatives, here we present some and present one that we have called generalized that allows us to put some of the others as a particular case of this but, what interests us is to determine that there…
Complex functions have multiple uses in various fields of study, so analyze their characteristics it is of extensive interest to other sciences. This work begins with a particular class of rational functions of a complex variable; over this…
We encounter a bottleneck when we try to borrow the strength of classical classifiers to classify functional data. The major issue is that functional data are intrinsically infinite dimensional, thus classical classifiers cannot be applied…
Multivariate functions emerge naturally in a wide variety of data-driven models. Popular choices are expressions in the form of basis expansions or neural networks. While highly effective, the resulting functions tend to be hard to…
Theoretical material investigation based on density functional theory (DFT) has been a breakthrough in the last century. Nevertheless, the optical properties calculated by DFT generally show poor agreement with experimental results…
This paper tackles one of the most fundamental goals in functional time series analysis which is to provide reliable predictions for future functions. Existing methods for predicting a complete future functional observation use only…
Automatic differentiation plays a prominent role in scientific computing and in modern machine learning, often in the context of powerful programming systems. The relation of the various embodiments of automatic differentiation to the…
Functional data analysis involves data described by regular functions rather than by a finite number of real valued variables. While some robust data analysis methods can be applied directly to the very high dimensional vectors obtained…
Multi-dimensional classification (MDC) can be employed in a range of applications where one needs to predict multiple class variables for each given instance. Many existing MDC methods suffer from at least one of inaccuracy, scalability,…