Modern randomization methods in clinical trials are invariably adaptive, meaning that the assignment of the next subject to a treatment group uses the accumulated information in the trial. Some of the recent adaptive randomization methods use mathematical programming to construct attractive clinical trials that balance the group features, such as their sizes and covariate distributions of their subjects. We review some of these methods and compare their performance with common covariate-adaptive randomization methods for small clinical trials. We introduce an energy distance measure that compares the discrepancy between the two groups using the joint distribution of the subjects' covariates. This metric is more appealing than evaluating the discrepancy between the groups using their marginal covariate distributions. Using numerical experiments, we demonstrate the advantages of the mathematical programming methods under the new measure. In the supplementary material, we provide R codes to reproduce our study results and facilitate comparisons of different randomization procedures.
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Reservoir computing is a machine learning framework that has been shown to be able to replicate the chaotic attractor, including the fractal dimension and the entire Lyapunov spectrum, of the dynamical system on which it is trained. We quantitatively relate the generalized synchronization dynamics of a driven reservoir during the training stage to the performance of the trained reservoir computer at the attractor reconstruction task. We show that, in order to obtain successful attractor reconstruction and Lyapunov spectrum estimation, the largest conditional Lyapunov exponent of the driven reservoir must be significantly more negative than the most negative Lyapunov exponent of the target system. We also find that the maximal conditional Lyapunov exponent of the reservoir depends strongly on the spectral radius of the reservoir adjacency matrix, and therefore, for attractor reconstruction and Lyapunov spectrum estimation, small spectral radius reservoir computers perform better in general. Our arguments are supported by numerical examples on well-known chaotic systems.
Developing algorithms for accurate and comprehensive neural decoding of mental contents is one of the long-cherished goals in the field of neuroscience and brain-machine interfaces. Previous studies have demonstrated the feasibility of neural decoding by training machine learning models to map brain activity patterns into a semantic vector representation of stimuli. These vectors, hereafter referred as pretrained feature vectors, are usually derived from semantic spaces based solely on image and/or text features and therefore they might have a totally different characteristics than how visual stimuli is represented in the human brain, resulting in limiting the capability of brain decoders to learn this mapping. To address this issue, we propose a representation learning framework, termed brain-grounding of semantic vectors, which fine-tunes pretrained feature vectors to better align with the neural representation of visual stimuli in the human brain. We trained this model this model with functional magnetic resonance imaging (fMRI) of 150 different visual stimuli categories, and then performed zero-shot brain decoding and identification analyses on 1) fMRI and 2) magnetoencephalography (MEG). Interestingly, we observed that by using the brain-grounded vectors, the brain decoding and identification accuracy on brain data from different neuroimaging modalities increases. These findings underscore the potential of incorporating a richer array of brain-derived features to enhance performance of brain decoding algorithms.
Regression analysis is a central topic in statistical modeling, aiming to estimate the relationships between a dependent variable, commonly referred to as the response variable, and one or more independent variables, i.e., explanatory variables. Linear regression is by far the most popular method for performing this task in several fields of research, such as prediction, forecasting, or causal inference. Beyond various classical methods to solve linear regression problems, such as Ordinary Least Squares, Ridge, or Lasso regressions - which are often the foundation for more advanced machine learning (ML) techniques - the latter have been successfully applied in this scenario without a formal definition of statistical significance. At most, permutation or classical analyses based on empirical measures (e.g., residuals or accuracy) have been conducted to reflect the greater ability of ML estimations for detection. In this paper, we introduce a method, named Statistical Agnostic Regression (SAR), for evaluating the statistical significance of an ML-based linear regression based on concentration inequalities of the actual risk using the analysis of the worst case. To achieve this goal, similar to the classification problem, we define a threshold to establish that there is sufficient evidence with a probability of at least 1-eta to conclude that there is a linear relationship in the population between the explanatory (feature) and the response (label) variables. Simulations in only two dimensions demonstrate the ability of the proposed agnostic test to provide a similar analysis of variance given by the classical $F$ test for the slope parameter.
Explainable AI is crucial in medical imaging. In the challenging field of neuroscience, visual topics present a high level of complexity, particularly within three-dimensional space. The application of neuroscience, which involves identifying brain sulcal features from MRI, faces significant hurdles due to varying annotation protocols among experts and the intricate three-dimension functionality of the brain. Consequently, traditional explainability approaches fall short in effectively validating and evaluating these networks. To address this, we first present a mathematical formulation delineating various categories of explanation needs across diverse computer vision tasks, categorized into self-explanatory, semi-explanatory, non-explanatory, and new-pattern learning applications based on the reliability of the validation protocol. With respect to this mathematical formulation, we propose a 3D explainability framework aimed at validating the outputs of deep learning networks in detecting the paracingulate sulcus an essential brain anatomical feature. The framework integrates local 3D explanations, global explanations through dimensionality reduction, concatenated global explanations, and statistical shape features, unveiling new insights into pattern learning. We trained and tested two advanced 3D deep learning networks on the challenging TOP-OSLO dataset, significantly improving sulcus detection accuracy, particularly on the left hemisphere. During evaluation with diverse annotation protocols for this dataset, we highlighted the crucial role of an unbiased annotation process in achieving precise predictions and effective pattern learning within our proposed 3D framework. The proposed framework not only annotates the variable sulcus but also uncovers hidden AI knowledge, promising to advance our understanding of brain anatomy and function.
Utilizing non-concurrent controls in the analysis of late-entering experimental arms in platform trials has recently received considerable attention, both on academic and regulatory levels. While incorporating this data can lead to increased power and lower required sample sizes, it might also introduce bias to the effect estimators if temporal drifts are present in the trial. Aiming to mitigate the potential calendar time bias, we propose various frequentist model-based approaches that leverage the non-concurrent control data, while adjusting for time trends. One of the currently available frequentist models incorporates time as a categorical fixed effect, separating the duration of the trial into periods, defined as time intervals bounded by any treatment arm entering or leaving the platform. In this work, we propose two extensions of this model. First, we consider an alternative definition of the time covariate by dividing the trial into fixed-length calendar time intervals. Second, we propose alternative methods to adjust for time trends. In particular, we investigate adjusting for autocorrelated random effects to account for dependency between closer time intervals and employing spline regression to model time with a smooth polynomial function. We evaluate the performance of the proposed approaches in a simulation study and illustrate their use by means of a case study.
Recently, the increasing availability of repeated measurements in biomedical studies has motivated the development of several statistical methods for the dynamic prediction of survival in settings where a large (potentially high-dimensional) number of longitudinal covariates is available. These methods differ in both how they model the longitudinal covariates trajectories, and how they specify the relationship between the longitudinal covariates and the survival outcome. Because these methods are still quite new, little is known about their applicability, limitations and performance when applied to real-world data. To investigate these questions, we present a comparison of the predictive performance of the aforementioned methods and two simpler prediction approaches to three datasets that differ in terms of outcome type, sample size, number of longitudinal covariates and length of follow-up. We discuss how different modelling choices can have an impact on the possibility to accommodate unbalanced study designs and on computing time, and compare the predictive performance of the different approaches using a range of performance measures and landmark times.
Quantum artificial intelligence is a frontier of artificial intelligence research, pioneering quantum AI-powered circuits to address problems beyond the reach of deep learning with classical architectures. This work implements a large-scale quantum-activated recurrent neural network possessing more than 3 trillion hardware nodes/cm$^2$, originating from repeatable atomic-scale nucleation dynamics in an amorphous material integrated on-chip, controlled with 0.07 nW electric power per readout channel. Compared to the best-performing reservoirs currently reported, this implementation increases the scale of the network by two orders of magnitude and reduces the power consumption by six, reaching power efficiencies in the range of the human brain, dissipating 0.2 nW/neuron. When interrogated by a classical input, the chip implements a large-scale hardware security model, enabling dictionary-free authentication secure against statistical inference attacks, including AI's present and future development, even for an adversary with a copy of all the classical components available. Experimental tests report 99.6% reliability, 100% user authentication accuracy, and an ideal 50% key uniqueness. Due to its quantum nature, the chip supports a bit density per feature size area three times higher than the best technology available, with the capacity to store more than $2^{1104}$ keys in a footprint of 1 cm$^2$. Such a quantum-powered platform could help counteract the emerging form of warfare led by the cybercrime industry in breaching authentication to target small to large-scale facilities, from private users to intelligent energy grids.
With advancement of medicine, alternative exposures or interventions are emerging with respect to a common outcome, and there are needs to formally test the difference in the associations of multiple exposures. We propose a duplication method-based multivariate Wald test in the Cox proportional hazard regression analyses to test the difference in the associations of multiple exposures with a same outcome. The proposed method applies to linear or categorical exposures. To illustrate our method, we applied our method to compare the associations between alignment to two different dietary patterns, either as continuous or quartile exposures, and incident chronic diseases, defined as a composite of CVD, cancer, and diabetes, in the Health Professional Follow-up Study. Relevant sample codes in R that implement the proposed approach are provided. The proposed duplication-method-based approach offers a flexible, formal statistical test of multiple exposures for the common outcome with minimal assumptions.
In many communication contexts, the capabilities of the involved actors cannot be known beforehand, whether it is a cell, a plant, an insect, or even a life form unknown to Earth. Regardless of the recipient, the message space and time scale could be too fast, too slow, too large, or too small and may never be decoded. Therefore, it pays to devise a way to encode messages agnostic of space and time scales. We propose the use of fractal functions as self-executable infinite-frequency carriers for sending messages, given their properties of structural self-similarity and scale invariance. We call it `fractal messaging'. Starting from a spatial embedding, we introduce a framework for a space-time scale-free messaging approach to this challenge. When considering a space and time-agnostic framework for message transmission, it would be interesting to encode a message such that it could be decoded at several spatio-temporal scales. Hence, the core idea of the framework proposed herein is to encode a binary message as waves along infinitely many frequencies (in power-like distributions) and amplitudes, transmit such a message, and then decode and reproduce it. To do so, the components of the Weierstrass function, a known fractal, are used as carriers of the message. Each component will have its amplitude modulated to embed the binary stream, allowing for a space-time-agnostic approach to messaging.
Existing statistical methods for the analysis of micro-randomized trials (MRTs) are designed to estimate causal excursion effects using data from a single MRT. In practice, however, researchers can often find previous MRTs that employ similar interventions. In this paper, we develop data integration methods that capitalize on this additional information, leading to statistical efficiency gains. To further increase efficiency, we demonstrate how to combine these approaches according to a generalization of multivariate precision weighting that allows for correlation between estimates, and we show that the resulting meta-estimator possesses an asymptotic optimality property. We illustrate our methods in simulation and in a case study involving two MRTs in the area of smoking cessation.
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