188 research outputs found
Multiscale adaptive smoothing models for the hemodynamic response function in fMRI
In the event-related functional magnetic resonance imaging (fMRI) data
analysis, there is an extensive interest in accurately and robustly estimating
the hemodynamic response function (HRF) and its associated statistics (e.g.,
the magnitude and duration of the activation). Most methods to date are
developed in the time domain and they have utilized almost exclusively the
temporal information of fMRI data without accounting for the spatial
information. The aim of this paper is to develop a multiscale adaptive
smoothing model (MASM) in the frequency domain by integrating the spatial and
frequency information to adaptively and accurately estimate HRFs pertaining to
each stimulus sequence across all voxels in a three-dimensional (3D) volume. We
use two sets of simulation studies and a real data set to examine the finite
sample performance of MASM in estimating HRFs. Our real and simulated data
analyses confirm that MASM outperforms several other state-of-the-art methods,
such as the smooth finite impulse response (sFIR) model.Comment: Published in at http://dx.doi.org/10.1214/12-AOAS609 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Beyond Scalar Treatment: A Causal Analysis of Hippocampal Atrophy on Behavioral Deficits in Alzheimer's Studies
Alzheimer's disease is a progressive form of dementia that results in
problems with memory, thinking and behavior. It often starts with abnormal
aggregation and deposition of beta-amyloid and tau, followed by neuronal damage
such as atrophy of the hippocampi, and finally leads to behavioral deficits.
Despite significant progress in finding biomarkers associated with behavioral
deficits, the underlying causal mechanism remains largely unknown. Here we
investigate whether and how hippocampal atrophy contributes to behavioral
deficits based on a large-scale observational study conducted by the
Alzheimer's Disease Neuroimaging Initiative (ADNI). As a key novelty, we use 2D
representations of the hippocampi, which allows us to better understand atrophy
associated with different subregions. It, however, introduces methodological
challenges as existing causal inference methods are not well suited for
exploiting structural information embedded in the 2D exposures. Moreover, our
data contain more than 6 million clinical and genetic covariates, necessitating
appropriate confounder selection methods. We hence develop a novel two-step
causal inference approach tailored for our ADNI data application. Analysis
results suggest that atrophy of CA1 and subiculum subregions may cause more
severe behavioral deficits compared to CA2 and CA3 subregions. We further
evaluate our method using simulations and provide theoretical guarantees
Reinforced Angle-Based Multicategory Support Vector Machines
The Support Vector Machine (SVM) is a very popular classification tool with many successful applications. It was originally designed for binary problems with desirable theoretical properties. Although there exist various Multicategory SVM (MSVM) extensions in the literature, some challenges remain. In particular, most existing MSVMs make use of k classification functions for a k-class problem, and the corresponding optimization problems are typically handled by existing quadratic programming solvers. In this paper, we propose a new group of MSVMs, namely the Reinforced Angle-based MSVMs (RAMSVMs), using an angle-based prediction rule with k − 1 functions directly. We prove that RAMSVMs can enjoy Fisher consistency. Moreover, we show that the RAMSVM can be implemented using the very efficient coordinate descent algorithm on its dual problem. Numerical experiments demonstrate that our method is highly competitive in terms of computational speed, as well as classification prediction performance. Supplemental materials for the article are available online
Nearest-Neighbor Sampling Based Conditional Independence Testing
The conditional randomization test (CRT) was recently proposed to test
whether two random variables X and Y are conditionally independent given random
variables Z. The CRT assumes that the conditional distribution of X given Z is
known under the null hypothesis and then it is compared to the distribution of
the observed samples of the original data. The aim of this paper is to develop
a novel alternative of CRT by using nearest-neighbor sampling without assuming
the exact form of the distribution of X given Z. Specifically, we utilize the
computationally efficient 1-nearest-neighbor to approximate the conditional
distribution that encodes the null hypothesis. Then, theoretically, we show
that the distribution of the generated samples is very close to the true
conditional distribution in terms of total variation distance. Furthermore, we
take the classifier-based conditional mutual information estimator as our test
statistic. The test statistic as an empirical fundamental information theoretic
quantity is able to well capture the conditional-dependence feature. We show
that our proposed test is computationally very fast, while controlling type I
and II errors quite well. Finally, we demonstrate the efficiency of our
proposed test in both synthetic and real data analyses.Comment: Accepted at AAAI 2023; 9 Pages, 3 Figures, 2 Table
Optimal treatment allocation for efficient policy evaluation in sequential decision making
A/B testing is critical for modern technological companies to evaluate the effectiveness of newly developed products against standard baselines. This paper studies optimal designs that aim to maximize the amount of information obtained from online experiments to estimate treatment effects accurately. We propose three optimal allocation strategies in a dynamic setting where treatments are sequentially assigned over time. These strategies are designed to minimize the variance of the treatment effect estimator when data follow a non-Markov decision process or a (time-varying) Markov decision process. We further develop estimation procedures based on existing off-policy evaluation (OPE) methods and conduct extensive experiments in various environments to demonstrate the effectiveness of the proposed methodologies. In theory, we prove the optimality of the proposed treatment allocation design and establish upper bounds for the mean squared errors of the resulting treatment effect estimator
Bayesian longitudinal low-rank regression models for imaging genetic data from longitudinal studies
To perform a joint analysis of multivariate neuroimaging phenotypes and candidate genetic markers obtained from longitudinal studies, we develop a Bayesian longitudinal low-rank regression (L2R2) model. The L2R2 model integrates three key methodologies: a low-rank matrix for approximating the high-dimensional regression coefficient matrices corresponding to the genetic main effects and their interactions with time, penalized splines for characterizing the overall time effect, and a sparse factor analysis model coupled with random effects for capturing within-subject spatio-temporal correlations of longitudinal phenotypes. Posterior computation proceeds via an efficient Markov chainMonte Carlo algorithm. Simulations show that the L2R2 model outperforms several other competing methods. We apply the L2R2 model to investigate the effect of single nucleotide polymorphisms (SNPs) on the top 10 and top 40 previously reported Alzheimer disease-associated genes. We also identify associations between the interactions of these SNPs with patient age and the tissue volumes of 93 regions of interest from patients’ brain images obtained from the Alzheimer’s Disease Neuroimaging Initiative
A Reinforcement Learning Framework for Time-Dependent Causal Effects Evaluation in A/B Testing
A/B testing, or online experiment is a standard business strategy to compare
a new product with an old one in pharmaceutical, technological, and traditional
industries. Major challenges arise in online experiments where there is only
one unit that receives a sequence of treatments over time. In those
experiments, the treatment at a given time impacts current outcome as well as
future outcomes. The aim of this paper is to introduce a reinforcement learning
framework for carrying A/B testing, while characterizing the long-term
treatment effects. Our proposed testing procedure allows for sequential
monitoring and online updating, so it is generally applicable to a variety of
treatment designs in different industries. In addition, we systematically
investigate the theoretical properties (e.g., asymptotic distribution and
power) of our testing procedure. Finally, we apply our framework to both
synthetic datasets and a real-world data example obtained from a ride-sharing
company to illustrate its usefulness
Dynamic causal effects evaluation in A/B testing with a reinforcement learning framework
A/B testing, or online experiment is a standard business strategy to compare a new product with an old one in pharmaceutical, technological, and traditional industries. Major challenges arise in online experiments of two-sided marketplace platforms (e.g., Uber) where there is only one unit that receives a sequence of treatments over time. In those experiments, the treatment at a given time impacts current outcome as well as future outcomes. The aim of this article is to introduce a reinforcement learning framework for carrying A/B testing in these experiments, while characterizing the long-term treatment effects. Our proposed testing procedure allows for sequential monitoring and online updating. It is generally applicable to a variety of treatment designs in different industries. In addition, we systematically investigate the theoretical properties (e.g., size and power) of our testing procedure. Finally, we apply our framework to both simulated data and a real-world data example obtained from a technological company to illustrate its advantage over the current practice. A Python implementation of our test is available at https://github.com/callmespring/CausalRL. Supplementary materials for this article are available online
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