Discovering Functional Dependencies from Mixed-Type Data

Mandros, Panagiotis; Kaltenpoth, David; Boley, Mario; Vreeken, Jilles

doi:10.1145/3394486.3403193

Cited by 8 publications

(3 citation statements)

References 21 publications

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“…The third class of methods first discretizes the continuous random variables and then calculates mutual information from the discretized variables [4,5,31]. Two recent approaches based on adaptive partitioning for mixed random variables have been proposed [2,17]. While Mandros et al [17] focus on mutual information and its application to functional dependency discovery, Cabeli et al [2], similar to us, build upon an MDL-based score to estimate MI and CMI, to which we compare in Sec.…”

Section: Related Workmentioning

confidence: 99%

“…Two recent approaches based on adaptive partitioning for mixed random variables have been proposed [2,17]. While Mandros et al [17] focus on mutual information and its application to functional dependency discovery, Cabeli et al [2], similar to us, build upon an MDL-based score to estimate MI and CMI, to which we compare in Sec. 7.…”

Section: Related Workmentioning

confidence: 99%

“…While estimating (conditional) mutual information for purely discrete or continuous data is a well-studied problem [4,5,8,10,22], many real-world settings concern a mix of discrete and continuous random variables, such as age (in years) and height, or even random variables that can individually consist of a mixture of discrete and continuous components. Although several discretization-based approaches that can estimate MI for a mix of discrete and continuous random variables have recently emerged [2,17,31], so far only methods based on k-nearest neighbour (kNN) estimation were shown to work on mixed variables, which may consist of discrete-continuous mixture variables [7,19,24].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Estimating Conditional Mutual Information for Discrete-Continuous Mixtures using Multi-Dimensional Adaptive Histograms

Yang¹,

Leeuwen²

2021

Proceedings of the 2021 SIAM International Conference on Data Mining (SDM)

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Estimating conditional mutual information (CMI) is an essential yet challenging step in many machine learning and data mining tasks. Estimating CMI from data that contains both discrete and continuous variables, or even discrete-continuous mixture variables, is a particularly hard problem. In this paper, we show that CMI for such mixture variables, defined based on the Radon-Nikodym derivate, can be written as a sum of entropies, just like CMI for purely discrete or continuous data. Further, we show that CMI can be consistently estimated for discrete-continuous mixture variables by learning an adaptive histogram model. In practice, we estimate such a model by iteratively discretizing the continuous data points in the mixture variables. To evaluate the performance of our estimator, we benchmark it against state-of-the-art CMI estimators as well as evaluate it in a causal discovery setting.

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Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Estimating Conditional Mutual Information for Discrete-Continuous Mixtures using Multi-Dimensional Adaptive Histograms

Yang¹,

Leeuwen²

2021

Proceedings of the 2021 SIAM International Conference on Data Mining (SDM)

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A KNN-Based Non-Parametric Conditional Independence Test for Mixed Data and Application in Causal Discovery

Huegle,

Hagedorn,

Schlosser

2023

Lecture Notes in Computer Science

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Feature selection on quantum computers

Sascha

Heese

Müller

et al. 2023

Quantum Mach. Intell.

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In machine learning, fewer features reduce model complexity. Carefully assessing the influence of each input feature on the model quality is therefore a crucial preprocessing step. We propose a novel feature selection algorithm based on a quadratic unconstrained binary optimization (QUBO) problem, which allows to select a specified number of features based on their importance and redundancy. In contrast to iterative or greedy methods, our direct approach yields higher-quality solutions. QUBO problems are particularly interesting because they can be solved on quantum hardware. To evaluate our proposed algorithm, we conduct a series of numerical experiments using a classical computer, a quantum gate computer, and a quantum annealer. Our evaluation compares our method to a range of standard methods on various benchmark data sets. We observe competitive performance.

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Discovering Functional Dependencies from Mixed-Type Data

Cited by 8 publications

References 21 publications

Estimating Conditional Mutual Information for Discrete-Continuous Mixtures using Multi-Dimensional Adaptive Histograms

Estimating Conditional Mutual Information for Discrete-Continuous Mixtures using Multi-Dimensional Adaptive Histograms

A KNN-Based Non-Parametric Conditional Independence Test for Mixed Data and Application in Causal Discovery

Feature selection on quantum computers

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