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Twin revolutions in wearable technologies and smartphone-delivered digital health interventions have significantly expanded the accessibility and uptake of mobile health (mHealth) interventions across various health science domains. Sequentially randomized experiments called micro-randomized trials (MRTs) have grown in popularity to empirically evaluate the effectiveness of these mHealth intervention components. MRTs have given rise to a new class of causal estimands known as "causal excursion effects", which enable health scientists to assess how intervention effectiveness changes over time or is moderated by individual characteristics, context, or responses in the past. However, current data analysis methods for estimating causal excursion effects require pre-specified features of the observed high-dimensional history to construct a working model of an important nuisance parameter. While machine learning algorithms are ideal for automatic feature construction, their naive application to causal excursion estimation can lead to bias under model misspecification, potentially yielding incorrect conclusions about intervention effectiveness. To address this issue, this paper revisits the estimation of causal excursion effects from a meta-learner perspective, where the analyst remains agnostic to the choices of supervised learning algorithms used to estimate nuisance parameters. The paper presents asymptotic properties of the novel estimators and compares them theoretically and through extensive simulation experiments, demonstrating relative efficiency gains and supporting the recommendation for a doubly robust alternative to existing methods. Finally, the practical utility of the proposed methods is demonstrated by analyzing data from a multi-institution cohort of first-year medical residents in the United States (NeCamp et al., 2020).

In this work we present a non-parametric online market regime detection method for multidimensional data structures using a path-wise two-sample test derived from a maximum mean discrepancy-based similarity metric on path space that uses rough path signatures as a feature map. The latter similarity metric has been developed and applied as a discriminator in recent generative models for small data environments, and has been optimised here to the setting where the size of new incoming data is particularly small, for faster reactivity. On the same principles, we also present a path-wise method for regime clustering which extends our previous work. The presented regime clustering techniques were designed as ex-ante market analysis tools that can identify periods of approximatively similar market activity, but the new results also apply to path-wise, high dimensional-, and to non-Markovian settings as well as to data structures that exhibit autocorrelation. We demonstrate our clustering tools on easily verifiable synthetic datasets of increasing complexity, and also show how the outlined regime detection techniques can be used as fast on-line automatic regime change detectors or as outlier detection tools, including a fully automated pipeline. Finally, we apply the fine-tuned algorithms to real-world historical data including high-dimensional baskets of equities and the recent price evolution of crypto assets, and we show that our methodology swiftly and accurately indicated historical periods of market turmoil.

Separating signals from an additive mixture may be an unnecessarily hard problem when one is only interested in specific properties of a given signal. In this work, we tackle simpler "statistical component separation" problems that focus on recovering a predefined set of statistical descriptors of a target signal from a noisy mixture. Assuming access to samples of the noise process, we investigate a method devised to match the statistics of the solution candidate corrupted by noise samples with those of the observed mixture. We first analyze the behavior of this method using simple examples with analytically tractable calculations. Then, we apply it in an image denoising context employing 1) wavelet-based descriptors, 2) ConvNet-based descriptors on astrophysics and ImageNet data. In the case of 1), we show that our method better recovers the descriptors of the target data than a standard denoising method in most situations. Additionally, despite not constructed for this purpose, it performs surprisingly well in terms of peak signal-to-noise ratio on full signal reconstruction. In comparison, representation 2) appears less suitable for image denoising. Finally, we extend this method by introducing a diffusive stepwise algorithm which gives a new perspective to the initial method and leads to promising results for image denoising under specific circumstances.

Existing theories on deep nonparametric regression have shown that when the input data lie on a low-dimensional manifold, deep neural networks can adapt to the intrinsic data structures. In real world applications, such an assumption of data lying exactly on a low dimensional manifold is stringent. This paper introduces a relaxed assumption that the input data are concentrated around a subset of $\mathbb{R}^d$ denoted by $\mathcal{S}$, and the intrinsic dimension of $\mathcal{S}$ can be characterized by a new complexity notation -- effective Minkowski dimension. We prove that, the sample complexity of deep nonparametric regression only depends on the effective Minkowski dimension of $\mathcal{S}$ denoted by $p$. We further illustrate our theoretical findings by considering nonparametric regression with an anisotropic Gaussian random design $N(0,\Sigma)$, where $\Sigma$ is full rank. When the eigenvalues of $\Sigma$ have an exponential or polynomial decay, the effective Minkowski dimension of such an Gaussian random design is $p=\mathcal{O}(\sqrt{\log n})$ or $p=\mathcal{O}(n^\gamma)$, respectively, where $n$ is the sample size and $\gamma\in(0,1)$ is a small constant depending on the polynomial decay rate. Our theory shows that, when the manifold assumption does not hold, deep neural networks can still adapt to the effective Minkowski dimension of the data, and circumvent the curse of the ambient dimensionality for moderate sample sizes.

Nowadays, the deployment of deep learning models on edge devices for addressing real-world classification problems is becoming more prevalent. Moreover, there is a growing popularity in the approach of early classification, a technique that involves classifying the input data after observing only an early portion of it, aiming to achieve reduced communication and computation requirements, which are crucial parameters in edge intelligence environments. While early classification in the field of time series analysis has been broadly researched, existing solutions for multivariate time series problems primarily focus on early classification along the temporal dimension, treating the multiple input channels in a collective manner. In this study, we propose a more flexible early classification pipeline that offers a more granular consideration of input channels and extends the early classification paradigm to the channel dimension. To implement this method, we utilize reinforcement learning techniques and introduce constraints to ensure the feasibility and practicality of our objective. To validate its effectiveness, we conduct experiments using synthetic data and we also evaluate its performance on real datasets. The comprehensive results from our experiments demonstrate that, for multiple datasets, our method can enhance the early classification paradigm by achieving improved accuracy for equal input utilization.

We develop a new model for spatial random field reconstruction of a binary-valued spatial phenomenon. In our model, sensors are deployed in a wireless sensor network across a large geographical region. Each sensor measures a non-Gaussian inhomogeneous temporal process which depends on the spatial phenomenon. Two types of sensors are employed: one collects point observations at specific time points, while the other collects integral observations over time intervals. Subsequently, the sensors transmit these time-series observations to a Fusion Center (FC), and the FC infers the spatial phenomenon from these observations. We show that the resulting posterior predictive distribution is intractable and develop a tractable two-step procedure to perform inference. Firstly, we develop algorithms to perform approximate Likelihood Ratio Tests on the time-series observations, compressing them to a single bit for both point sensors and integral sensors. Secondly, once the compressed observations are transmitted to the FC, we utilize a Spatial Best Linear Unbiased Estimator (S-BLUE) to reconstruct the binary spatial random field at any desired spatial location. The performance of the proposed approach is studied using simulation. We further illustrate the effectiveness of our method using a weather dataset from the National Environment Agency (NEA) of Singapore with fields including temperature and relative humidity.

In multivariate time series analysis, the coherence measures the linear dependency between two-time series at different frequencies. However, real data applications often exhibit nonlinear dependency in the frequency domain. Conventional coherence analysis fails to capture such dependency. The quantile coherence, on the other hand, characterizes nonlinear dependency by defining the coherence at a set of quantile levels based on trigonometric quantile regression. Although quantile coherence is a more powerful tool, its estimation remains challenging due to the high level of noise. This paper introduces a new estimation technique for quantile coherence. The proposed method is semi-parametric, which uses the parametric form of the spectrum of the vector autoregressive (VAR) model as an approximation to the quantile spectral matrix, along with nonparametric smoothing across quantiles. For each fixed quantile level, we obtain the VAR parameters from the quantile periodograms, then, using the Durbin-Levinson algorithm, we calculate the preliminary estimate of quantile coherence using the VAR parameters. Finally, we smooth the preliminary estimate of quantile coherence across quantiles using a nonparametric smoother. Numerical results show that the proposed estimation method outperforms nonparametric methods. We show that quantile coherence-based bivariate time series clustering has advantages over the ordinary VAR coherence. For applications, the identified clusters of financial stocks by quantile coherence with a market benchmark are shown to have an intriguing and more accurate structure of diversified investment portfolios that may be used by investors to make better decisions.

This paper proposes an adaptive penalized weighted mean regression for outlier detection of high-dimensional data. In comparison to existing approaches based on the mean shift model, the proposed estimators demonstrate robustness against outliers present in both response variables and/or covariates. By utilizing the adaptive Huber loss function, the proposed method is effective in high-dimensional linear models characterized by heavy-tailed and heteroscedastic error distributions. The proposed framework enables simultaneous and collaborative estimation of regression parameters and outlier detection. Under regularity conditions, outlier detection consistency and oracle inequalities of robust estimates in high-dimensional settings are established. Additionally, theoretical robustness properties, such as the breakdown point and a smoothed limiting influence function, are ascertained. Extensive simulation studies and a breast cancer survival data are used to evaluate the numerical performance of the proposed method, demonstrating comparable or superior variable selection and outlier detection capabilities.

This paper presents a novel approach to Bayesian nonparametric spectral analysis of stationary multivariate time series. Starting with a parametric vector-autoregressive model, the parametric likelihood is nonparametrically adjusted in the frequency domain to account for potential deviations from parametric assumptions. We show mutual contiguity of the nonparametrically corrected likelihood, the multivariate Whittle likelihood approximation and the exact likelihood for Gaussian time series. A multivariate extension of the nonparametric Bernstein-Dirichlet process prior for univariate spectral densities to the space of Hermitian positive definite spectral density matrices is specified directly on the correction matrices. An infinite series representation of this prior is then used to develop a Markov chain Monte Carlo algorithm to sample from the posterior distribution. The code is made publicly available for ease of use and reproducibility. With this novel approach we provide a generalization of the multivariate Whittle-likelihood-based method of Meier et al. (2020) as well as an extension of the nonparametrically corrected likelihood for univariate stationary time series of Kirch et al. (2019) to the multivariate case. We demonstrate that the nonparametrically corrected likelihood combines the efficiencies of a parametric with the robustness of a nonparametric model. Its numerical accuracy is illustrated in a comprehensive simulation study. We illustrate its practical advantages by a spectral analysis of two environmental time series data sets: a bivariate time series of the Southern Oscillation Index and fish recruitment and time series of windspeed data at six locations in California.

We propose a model to flexibly estimate joint tail properties by exploiting the convergence of an appropriately scaled point cloud onto a compact limit set. Characteristics of the shape of the limit set correspond to key tail dependence properties. We directly model the shape of the limit set using B\'ezier splines, which allow flexible and parsimonious specification of shapes in two dimensions. We then fit the B\'ezier splines to data in pseudo-polar coordinates using Markov chain Monte Carlo, utilizing a limiting approximation to the conditional likelihood of the radii given angles. By imposing appropriate constraints on the parameters of the B\'ezier splines, we guarantee that each posterior sample is a valid limit set boundary, allowing direct posterior analysis of any quantity derived from the shape of the curve. Furthermore, we obtain interpretable inference on the asymptotic dependence class by using mixture priors with point masses on the corner of the unit box. Finally, we apply our model to bivariate datasets of extremes of variables related to fire risk and air pollution.