3 research outputs found
Testing exchangeability by pairwise betting
In this paper, we address the problem of testing exchangeability of a
sequence of random variables, . This problem has been studied
under the recently popular framework of testing by betting. But the mapping of
testing problems to game is not one to one: many games can be designed for the
same test. Past work established that it is futile to play single game betting
on every observation: test martingales in the data filtration are powerless.
Two avenues have been explored to circumvent this impossibility: betting in a
reduced filtration (wealth is a test martingale in a coarsened filtration), or
playing many games in parallel (wealth is an e-process in the data filtration).
The former has proved to be difficult to theoretically analyze, while the
latter only works for binary or discrete observation spaces. Here, we introduce
a different approach that circumvents both drawbacks. We design a new (yet
simple) game in which we observe the data sequence in pairs. Despite the fact
that betting on individual observations is futile, we show that betting on
pairs of observations is not. To elaborate, we prove that our game leads to a
nontrivial test martingale, which is interesting because it has been obtained
by shrinking the filtration very slightly. We show that our test controls
type-1 error despite continuous monitoring, and achieves power one for both
binary and continuous observations, under a broad class of alternatives. Due to
the shrunk filtration, optional stopping is only allowed at even stopping
times, not at odd ones: a relatively minor price. We provide a wide array of
simulations that align with our theoretical findings
Group-Feature (Sensor) Selection With Controlled Redundancy Using Neural Networks
In this paper, we present a novel embedded feature selection method based on
a Multi-layer Perceptron (MLP) network and generalize it for group-feature or
sensor selection problems, which can control the level of redundancy among the
selected features or groups. Additionally, we have generalized the group lasso
penalty for feature selection to encompass a mechanism for selecting valuable
group features while simultaneously maintaining a control over redundancy. We
establish the monotonicity and convergence of the proposed algorithm, with a
smoothed version of the penalty terms, under suitable assumptions. Experimental
results on several benchmark datasets demonstrate the promising performance of
the proposed methodology for both feature selection and group feature selection
over some state-of-the-art methods
Robust Classification of High-Dimensional Data using Data-Adaptive Energy Distance
Classification of high-dimensional low sample size (HDLSS) data poses a
challenge in a variety of real-world situations, such as gene expression
studies, cancer research, and medical imaging. This article presents the
development and analysis of some classifiers that are specifically designed for
HDLSS data. These classifiers are free of tuning parameters and are robust, in
the sense that they are devoid of any moment conditions of the underlying data
distributions. It is shown that they yield perfect classification in the HDLSS
asymptotic regime, under some fairly general conditions. The comparative
performance of the proposed classifiers is also investigated. Our theoretical
results are supported by extensive simulation studies and real data analysis,
which demonstrate promising advantages of the proposed classification
techniques over several widely recognized methods.Comment: Accepted to be published at the European Conference on Machine
Learning and Principles and Practice of Knowledge Discovery in Databases
(ECML PKDD), 202