Related papers: A Grammar of Data Analysis
Background: The past few years have seen a tremendous increase in the size and complexity of datasets. Scientific and clinical studies must to incorporate datasets that cross multiple spatial and temporal scales to describe a particular…
R is a language and computing environment that has been developed for data manipulation, statistical computing, and scientific graphing. In the paper, we demonstrate its use analyzing data collected in a few experiments taken from an…
We use the notion of topological data analysis to compare metrics on data sets. We provide two different motivating examples for this. The first of these is a point cloud data set that has $\mathbb{R}^2$ as its ambient space, and is…
The ability to read, write, and speak mathematics is critical to students becoming comfortable with statistical models and skills. Faster development of those skills may act as encouragement to further engage with the discipline. Vocabulary…
Data leakage has been identified in 648 published machine learning papers across 30 scientific fields. The knowledge to prevent it exists; the tools do not enforce it. This paper presents a grammar - eight typed primitives, a directed…
In this article, we present a fresh perspective on language, combining ideas from various sources, but mixed in a new synthesis. As in the minimalist program, the question is whether we can formulate an elegant formalism, a universal…
Graphs are a generalized concept that encompasses more complex data structures than trees, such as difference lists, doubly-linked lists, skip lists, and leaf-linked trees. Normally, these structures are handled with destructive assignments…
Machine Learning produces efficient decision and prediction models based on input-output data only. Such models have the form of decision trees or neural nets and are far from transparent analytical models, based on mathematical formulas.…
Knowing the precise format of a program's input is a necessary prerequisite for systematic testing. Given a program and a small set of sample inputs, we (1) track the data flow of inputs to aggregate input fragments that share the same data…
Data analyses are often constructed in an imperative manner, where commands representing actions taken on the data are issued sequentially. The publication of these commands, along with the data, is essential to the reproducibility of the…
In some contexts, well-formed natural language cannot be expected as input to information or communication systems. In these contexts, the use of grammar-independent input (sequences of uninflected semantic units like e.g.…
The determination of block-entropies is a well established method for the investigation of discrete data, also called symbols (7). There is a large variety of such symbolic sequences, ranging from texts written in natural languages,…
We reformulate minimalist grammars as partial functions on term algebras for strings and trees. Using filler/role bindings and tensor product representations, we construct homomorphisms for these data structures into geometric vector…
Formal grammars are extensively used in Computer Science and related fields to study the rules which govern production of a language. The use of these grammars can be extended beyond mere language production. One possibility is to view…
We define a class of probabilistic models in terms of an operator algebra of stochastic processes, and a representation for this class in terms of stochastic parameterized grammars. A syntactic specification of a grammar is mapped to…
We provide an analytical argument for understanding the likely nature of parameter shifts between those coming from an analysis of a dataset and from a subset of that dataset, assuming differences are down to noise and any intrinsic…
Practical data analysis involves many implicit or explicit assumptions about the good behavior of the data, and excludes consideration of various potentially pathological or limit cases. In this work, we present a new general theory of…
Chart annotations enhance visualization accessibility but suffer from fragmented, non-standardized representations that limit cross-platform reuse. We propose ChartMark, a structured grammar that separates annotation semantics from…
Usually, probabilistic automata and probabilistic grammars have crisp symbols as inputs, which can be viewed as the formal models of computing with values. In this paper, we first introduce probabilistic automata and probabilistic grammars…
This article provides an overview on the statistical modeling of complex data as increasingly encountered in modern data analysis. It is argued that such data can often be described as elements of a metric space that satisfies certain…