Simultaneously identifying contributory variables and controlling the false discovery rate (FDR) in high-dimensional data is an important statistical problem. In this paper, we propose a novel model-free variable selection procedure in sufficient dimension reduction via data splitting technique. The variable selection problem is first connected with a least square procedure with several response transformations. We construct a series of statistics with global symmetry property and then utilize the symmetry to derive a data-driven threshold to achieve error rate control. This method can achieve finite-sample and asymptotic FDR control under some mild conditions. Numerical experiments indicate that our procedure has satisfactory FDR control and higher power compared with existing methods.
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Recurrent neural networks (RNNs) in the brain and in silico excel at solving tasks with intricate temporal dependencies. Long timescales required for solving such tasks can arise from properties of individual neurons (single-neuron timescale, $\tau$, e.g., membrane time constant in biological neurons) or recurrent interactions among them (network-mediated timescale). However, the contribution of each mechanism for optimally solving memory-dependent tasks remains poorly understood. Here, we train RNNs to solve $N$-parity and $N$-delayed match-to-sample tasks with increasing memory requirements controlled by $N$ by simultaneously optimizing recurrent weights and $\tau$s. We find that for both tasks RNNs develop longer timescales with increasing $N$, but depending on the learning objective, they use different mechanisms. Two distinct curricula define learning objectives: sequential learning of a single-$N$ (single-head) or simultaneous learning of multiple $N$s (multi-head). Single-head networks increase their $\tau$ with $N$ and are able to solve tasks for large $N$, but they suffer from catastrophic forgetting. However, multi-head networks, which are explicitly required to hold multiple concurrent memories, keep $\tau$ constant and develop longer timescales through recurrent connectivity. Moreover, we show that the multi-head curriculum increases training speed and network stability to ablations and perturbations, and allows RNNs to generalize better to tasks beyond their training regime. This curriculum also significantly improves training GRUs and LSTMs for large-$N$ tasks. Our results suggest that adapting timescales to task requirements via recurrent interactions allows learning more complex objectives and improves the RNN's performance.
Discovering causal relationships from observational data is a fundamental yet challenging task. In some applications, it may suffice to learn the causal features of a given response variable, instead of learning the entire underlying causal structure. Invariant causal prediction (ICP, Peters et al., 2016) is a method for causal feature selection which requires data from heterogeneous settings. ICP assumes that the mechanism for generating the response from its direct causes is the same in all settings and exploits this invariance to output a subset of the causal features. The framework of ICP has been extended to general additive noise models and to nonparametric settings using conditional independence testing. However, nonparametric conditional independence testing often suffers from low power (or poor type I error control) and the aforementioned parametric models are not suitable for applications in which the response is not measured on a continuous scale, but rather reflects categories or counts. To bridge this gap, we develop ICP in the context of transformation models (TRAMs), allowing for continuous, categorical, count-type, and uninformatively censored responses (we show that, in general, these model classes do not allow for identifiability when there is no exogenous heterogeneity). We propose TRAM-GCM, a test for invariance of a subset of covariates, based on the expected conditional covariance between environments and score residuals which satisfies uniform asymptotic level guarantees. For the special case of linear shift TRAMs, we propose an additional invariance test, TRAM-Wald, based on the Wald statistic. We implement both proposed methods in the open-source R package "tramicp" and show in simulations that under the correct model specification, our approach empirically yields higher power than nonparametric ICP based on conditional independence testing.
Sequential change detection is a classical problem with a variety of applications. However, the majority of prior work has been parametric, for example, focusing on exponential families. We develop a fundamentally new and general framework for sequential change detection when the pre- and post-change distributions are nonparametrically specified (and thus composite). Our procedures come with clean, nonasymptotic bounds on the average run length (frequency of false alarms). In certain nonparametric cases (like sub-Gaussian or sub-exponential), we also provide near-optimal bounds on the detection delay following a changepoint. The primary technical tool that we introduce is called an \emph{e-detector}, which is composed of sums of e-processes -- a fundamental generalization of nonnegative supermartingales -- that are started at consecutive times. We first introduce simple Shiryaev-Roberts and CUSUM-style e-detectors, and then show how to design their mixtures in order to achieve both statistical and computational efficiency. Our e-detector framework can be instantiated to recover classical likelihood-based procedures for parametric problems, as well as yielding the first change detection method for many nonparametric problems. As a running example, we tackle the problem of detecting changes in the mean of a bounded random variable without i.i.d. assumptions, with an application to tracking the performance of a basketball team over multiple seasons.
We give a short survey of recent results on sparse-grid linear algorithms of approximate recovery and integration of functions possessing a unweighted or weighted Sobolev mixed smoothness based on their sampled values at a certain finite set. Some of them are extended to more general cases.
Nonlinear tracking control enabling a dynamical system to track a desired trajectory is fundamental to robotics, serving a wide range of civil and defense applications. In control engineering, designing tracking control requires complete knowledge of the system model and equations. We develop a model-free, machine-learning framework to control a two-arm robotic manipulator using only partially observed states, where the controller is realized by reservoir computing. Stochastic input is exploited for training, which consists of the observed partial state vector as the first and its immediate future as the second component so that the neural machine regards the latter as the future state of the former. In the testing (deployment) phase, the immediate-future component is replaced by the desired observational vector from the reference trajectory. We demonstrate the effectiveness of the control framework using a variety of periodic and chaotic signals, and establish its robustness against measurement noise, disturbances, and uncertainties.
Point source localisation is generally modelled as a Lasso-type problem on measures. However, optimisation methods in non-Hilbert spaces, such as the space of Radon measures, are much less developed than in Hilbert spaces. Most numerical algorithms for point source localisation are based on the Frank-Wolfe conditional gradient method, for which ad hoc convergence theory is developed. We develop extensions of proximal-type methods to spaces of measures. This includes forward-backward splitting, its inertial version, and primal-dual proximal splitting. Their convergence proofs follow standard patterns. We demonstrate their numerical efficacy.
We examine a stochastic formulation for data-driven optimization wherein the decision-maker is not privy to the true distribution, but has knowledge that it lies in some hypothesis set and possesses a historical data set, from which information about it can be gleaned. We define a prescriptive solution as a decision rule mapping such a data set to decisions. As there does not exist prescriptive solutions that are generalizable over the entire hypothesis set, we define out-of-sample optimality as a local average over a neighbourhood of hypotheses, and averaged over the sampling distribution. We prove sufficient conditions for local out-of-sample optimality, which reduces to functions of the sufficient statistic of the hypothesis family. We present an optimization problem that would solve for such an out-of-sample optimal solution, and does so efficiently by a combination of sampling and bisection search algorithms. Finally, we illustrate our model on the newsvendor model, and find strong performance when compared against alternatives in the literature. There are potential implications of our research on end-to-end learning and Bayesian optimization.
Image-based systems have gained popularity owing to their capacity to provide rich manufacturing status information, low implementation costs and high acquisition rates. However, the complexity of the image background and various anomaly patterns pose new challenges to existing matrix decomposition methods, which are inadequate for modeling requirements. Moreover, the uncertainty of the anomaly can cause anomaly contamination problems, making the designed model and method highly susceptible to external disturbances. To address these challenges, we propose a two-stage strategy anomaly detection method that detects anomalies by identifying suspected patches (Ano-SuPs). Specifically, we propose to detect the patches with anomalies by reconstructing the input image twice: the first step is to obtain a set of normal patches by removing those suspected patches, and the second step is to use those normal patches to refine the identification of the patches with anomalies. To demonstrate its effectiveness, we evaluate the proposed method systematically through simulation experiments and case studies. We further identified the key parameters and designed steps that impact the model's performance and efficiency.
In this study, we propose a staging area for ingesting new superconductors' experimental data in SuperCon that is machine-collected from scientific articles. Our objective is to enhance the efficiency of updating SuperCon while maintaining or enhancing the data quality. We present a semi-automatic staging area driven by a workflow combining automatic and manual processes on the extracted database. An anomaly detection automatic process aims to pre-screen the collected data. Users can then manually correct any errors through a user interface tailored to simplify the data verification on the original PDF documents. Additionally, when a record is corrected, its raw data is collected and utilised to improve machine learning models as training data. Evaluation experiments demonstrate that our staging area significantly improves curation quality. We compare the interface with the traditional manual approach of reading PDF documents and recording information in an Excel document. Using the interface boosts the precision and recall by 6% and 50%, respectively to an average increase of 40% in F1-score.
In large-scale systems there are fundamental challenges when centralised techniques are used for task allocation. The number of interactions is limited by resource constraints such as on computation, storage, and network communication. We can increase scalability by implementing the system as a distributed task-allocation system, sharing tasks across many agents. However, this also increases the resource cost of communications and synchronisation, and is difficult to scale. In this paper we present four algorithms to solve these problems. The combination of these algorithms enable each agent to improve their task allocation strategy through reinforcement learning, while changing how much they explore the system in response to how optimal they believe their current strategy is, given their past experience. We focus on distributed agent systems where the agents' behaviours are constrained by resource usage limits, limiting agents to local rather than system-wide knowledge. We evaluate these algorithms in a simulated environment where agents are given a task composed of multiple subtasks that must be allocated to other agents with differing capabilities, to then carry out those tasks. We also simulate real-life system effects such as networking instability. Our solution is shown to solve the task allocation problem to 6.7% of the theoretical optimal within the system configurations considered. It provides 5x better performance recovery over no-knowledge retention approaches when system connectivity is impacted, and is tested against systems up to 100 agents with less than a 9% impact on the algorithms' performance.
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