Statistical Depth Meets Machine Learning: Kernel Mean Embeddings and
Depth in Functional Data Analysis
- URL: http://arxiv.org/abs/2105.12778v1
- Date: Wed, 26 May 2021 18:22:33 GMT
- Title: Statistical Depth Meets Machine Learning: Kernel Mean Embeddings and
Depth in Functional Data Analysis
- Authors: George Wynne and Stanislav Nagy
- Abstract summary: Common $h$-depth and related statistical depths for functional data can be viewed as a kernel mean embedding.
This article highlights how the common $h$-depth and related statistical depths for functional data can be viewed as a kernel mean embedding.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Statistical depth is the act of gauging how representative a point is
compared to a reference probability measure. The depth allows introducing
rankings and orderings to data living in multivariate, or function spaces.
Though widely applied and with much experimental success, little theoretical
progress has been made in analysing functional depths. This article highlights
how the common $h$-depth and related statistical depths for functional data can
be viewed as a kernel mean embedding, a technique used widely in statistical
machine learning. This connection facilitates answers to open questions
regarding statistical properties of functional depths, as well as it provides a
link between the depth and empirical characteristic function based procedures
for functional data.
Related papers
- Computable Stability for Persistence Rank Function Machine Learning [0.0]
We study the performance of rank functions in functional inferential statistics and machine learning on both simulated and real data.
We find that the use of persistent homology captured by rank functions offers a clear improvement over existing approaches.
arXiv Detail & Related papers (2023-07-06T10:34:52Z) - Deep networks for system identification: a Survey [56.34005280792013]
System identification learns mathematical descriptions of dynamic systems from input-output data.
Main aim of the identified model is to predict new data from previous observations.
We discuss architectures commonly adopted in the literature, like feedforward, convolutional, and recurrent networks.
arXiv Detail & Related papers (2023-01-30T12:38:31Z) - MARS: Meta-Learning as Score Matching in the Function Space [79.73213540203389]
We present a novel approach to extracting inductive biases from a set of related datasets.
We use functional Bayesian neural network inference, which views the prior as a process and performs inference in the function space.
Our approach can seamlessly acquire and represent complex prior knowledge by metalearning the score function of the data-generating process.
arXiv Detail & Related papers (2022-10-24T15:14:26Z) - Offline Reinforcement Learning with Differentiable Function
Approximation is Provably Efficient [65.08966446962845]
offline reinforcement learning, which aims at optimizing decision-making strategies with historical data, has been extensively applied in real-life applications.
We take a step by considering offline reinforcement learning with differentiable function class approximation (DFA)
Most importantly, we show offline differentiable function approximation is provably efficient by analyzing the pessimistic fitted Q-learning algorithm.
arXiv Detail & Related papers (2022-10-03T07:59:42Z) - Embedding Functional Data: Multidimensional Scaling and Manifold
Learning [6.726255259929498]
We focus on classical scaling and Isomap -- prototypical methods that have played important roles in these area.
In the process, we highlight the crucial role that the ambient metric plays.
arXiv Detail & Related papers (2022-08-30T21:12:31Z) - Measuring Statistical Dependencies via Maximum Norm and Characteristic
Functions [0.0]
We propose a statistical dependence measure based on the maximum-norm of the difference between joint and product-marginal characteristic functions.
The proposed measure can detect arbitrary statistical dependence between two random vectors of possibly different dimensions.
We conduct experiments both with simulated and real data.
arXiv Detail & Related papers (2022-08-16T20:24:31Z) - A geometric perspective on functional outlier detection [0.0]
We develop a conceptualization of functional outlier detection that is more widely applicable and realistic than previously proposed.
We show that simple manifold learning methods can be used to reliably infer and visualize the geometric structure of functional data sets.
Our experiments on synthetic and real data sets demonstrate that this approach leads to outlier detection performances at least on par with existing functional data-specific methods.
arXiv Detail & Related papers (2021-09-14T17:42:57Z) - Ranking the information content of distance measures [61.754016309475745]
We introduce a statistical test that can assess the relative information retained when using two different distance measures.
This in turn allows finding the most informative distance measure out of a pool of candidates.
arXiv Detail & Related papers (2021-04-30T15:57:57Z) - More data or more parameters? Investigating the effect of data structure
on generalization [17.249712222764085]
Properties of data impact the test error as a function of the number of training examples and number of training parameters.
We show that noise in the labels and strong anisotropy of the input data play similar roles on the test error.
arXiv Detail & Related papers (2021-03-09T16:08:41Z) - Estimating Structural Target Functions using Machine Learning and
Influence Functions [103.47897241856603]
We propose a new framework for statistical machine learning of target functions arising as identifiable functionals from statistical models.
This framework is problem- and model-agnostic and can be used to estimate a broad variety of target parameters of interest in applied statistics.
We put particular focus on so-called coarsening at random/doubly robust problems with partially unobserved information.
arXiv Detail & Related papers (2020-08-14T16:48:29Z) - UNIPoint: Universally Approximating Point Processes Intensities [125.08205865536577]
We provide a proof that a class of learnable functions can universally approximate any valid intensity function.
We implement UNIPoint, a novel neural point process model, using recurrent neural networks to parameterise sums of basis function upon each event.
arXiv Detail & Related papers (2020-07-28T09:31:56Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.