We study the algorithmic problem of robust Gaussian mean estimation in the mean-shift contamination model with unknown covariance. Specifically, we are allowed to draw samples from a statistical mixture of an unknown target Gaussian $\mathcal{N}(\mu, \Sigma)$ (with weight at least $1-\alpha$), and arbitrary unknown mean-shifts of it, i.e., ${\mathcal{N}(\mu_i, \Sigma)}_i$, and the goal is to estimate $\mu$ up to any desired accuracy $\epsilon$ in $\ell_2$-norm. In the special case where $\Sigma$ is known to be the identity, prior work gave an algorithm with a near-optimal sample complexity of $\mathrm{poly}(d,2^{\epsilon^{-2}})$ and sample-polynomial time. In this work, we provide a quasi-polynomial time algorithm with sample complexity $2^{\mathrm{poly}(\log d/\epsilon)}$ in the more general unknown covariance case, markedly improving upon the only previously known estimator for this setting that incurs exponential runtime.

We initiate a systematic investigation of distribution testing in the framework of algorithmic replicability. Specifically, given independent samples from a collection of probability distributions, the goal is to characterize the sample complexity of replicably testing natural properties of the underlying distributions. On the algorithmic front, we develop new replicable algorithms for testing closeness and independence of discrete distributions. On the lower bound front, we develop a new methodology for proving sample complexity lower bounds for replicable testing that may be of broader interest. As an application of our technique, we establish near-optimal sample complexity lower bounds for replicable uniformity testing---answering an open question from prior work---and closeness testing.

The proliferation of virtual reality (VR) has led to its increasing adoption as an immersive medium for delivering presentations, distinct from other VR experiences like games and 360-degree videos by sharing information in richly interactive environments. However, creating engaging VR presentations remains a challenging and time-consuming task for users, hindering the full realization of VR presentation's capabilities. This research aims to explore the potential of VR presentation, analyze users' opinions, and investigate these via providing a user-friendly no-coding authoring tool. Through an examination of popular presentation software and interviews with seven professionals, we identified five design aspects and four design challenges for VR presentations. Based on the findings, we developed VRStory, a prototype for presentation authoring without coding to explore the design aspects and strategies for addressing the challenges. VRStory offers a variety of predefined and customizable VR elements, as well as modules for layout design, navigation control, and asset generation. A user study was then conducted with 12 participants to investigate their opinions and authoring experience with VRStory. Our results demonstrated that, while acknowledging the advantages of immersive and spatial features in VR, users often have a consistent mental model for traditional 2D presentations and may still prefer planar and static formats in VR for better accessibility and efficient communication. We finally shared our learned design considerations for future development of VR presentation tools, emphasizing the importance of balancing of promoting immersive features and ensuring accessibility.

Forecasting behavioral patterns can help humans comprehend their habits and tendencies, allowing them to inter-vene before problems arise. Among the numerous techniques of modeling human behavior, cyclic modeling can better identify recurring patterns, providing regularity and predictability in human behavior. However, existing approaches to cyclic modeling ignore the effects of human characteristics, such as resilience and coping abilities, which substantially influence the stability of behavior. To explore the value of adding such information in behavior modeling and prediction, we introduce a transformer-based architecture with an advanced attention mechanism and parallel operation that models regularity in human behavior from multidimensional sensing signals and predicts future behavior patterns. The architecture further transforms static human characteristics metadata into dynamic time series that conform to behavioral patterns and serve as covariates to assist prediction. Our experiments with a wearable dataset indicate that our architecture 1) is more accurate in forecasting human behavior patterns than current time-series models and 2) enables us to investigate the impact of human characteristics on behavior patterns. Specifically, we analyze the influence of resilience and coping strategies on behavioral regularity and predictability. We show that supplementing bio-behavioral wearable data with resilience and coping scores in the forecasting model increases the convergence speed of the model and decreases prediction loss.