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Recently, high dimensional vector auto-regressive models (VAR), have attracted a lot of interest, due to novel applications in the health, engineering and social sciences. The presence of temporal dependence poses additional challenges to the theory of penalized estimation techniques widely used in the analysis of their iid counterparts. However, recent work (e.g., [Basu and Michailidis, 2015, Kock and Callot, 2015]) has established optimal consistency of $\ell_1$-LASSO regularized estimates applied to models involving high dimensional stable, Gaussian processes. The only price paid for temporal dependence is an extra multiplicative factor that equals 1 for independent and identically distributed (iid) data. Further, [Wong et al., 2020] extended these results to heavy tailed VARs that exhibit "$\beta$-mixing" dependence, but the rates rates are sub-optimal, while the extra factor is intractable. This paper improves these results in two important directions: (i) We establish optimal consistency rates and corresponding finite sample bounds for the underlying model parameters that match those for iid data, modulo a price for temporal dependence, that is easy to interpret and equals 1 for iid data. (ii) We incorporate more general penalties in estimation (which are not decomposable unlike the $\ell_1$ norm) to induce general sparsity patterns. The key technical tool employed is a novel, easy-to-use concentration bound for heavy tailed linear processes, that do not rely on "mixing" notions and give tighter bounds.

Investigators are increasingly using novel methods for extending (generalizing or transporting) causal inferences from a trial to a target population. In many generalizability and transportability analyses, the trial and the observational data from the target population are separately sampled, following a non-nested trial design. In practical implementations of this design, non-randomized individuals from the target population are often identified by conditioning on the use of a particular treatment, while individuals who used other candidate treatments for the same indication or individuals who did not use any treatment are excluded. In this paper, we argue that conditioning on treatment in the target population changes the estimand of generalizability and transportability analyses and potentially introduces serious bias in the estimation of causal estimands in the target population or the subset of the target population using a specific treatment. Furthermore, we argue that the naive application of marginalization-based or weighting-based standardization methods does not produce estimates of any reasonable causal estimand. We use causal graphs and counterfactual arguments to characterize the identification problems induced by conditioning on treatment in the target population and illustrate the problems using simulated data. We conclude by considering the implications of our findings for applied work.

The significant presence of demand charges in electric bills motivates large-load customers to utilize energy storage to reduce the peak procurement from the grid. We herein study the problem of energy storage allocation for peak minimization, under the online setting where irrevocable decisions are sequentially made without knowing future demands. The problem is uniquely challenging due to (i) the coupling of online decisions across time imposed by the inventory constraints and (ii) the noncumulative nature of the peak procurement. We apply the CR-Pursuit framework and address the challenges unique to our minimization problem to design an online algorithm achieving the optimal competitive ratio (CR) among all online algorithms. We show that the optimal CR can be computed in polynomial time by solving a linear number of linear-fractional problems. More importantly, we generalize our approach to develop an \emph{anytime-optimal} online algorithm that achieves the best possible CR at any epoch, given the inputs and online decisions so far. The algorithm retains the optimal worst-case performance and attains adaptive average-case performance. Trace-driven simulations show that our algorithm can decrease the peak demand by an extra 19% compared to baseline alternatives under typical settings.

Binary stars undergo a variety of interactions and evolutionary phases, critical for predicting and explaining observed properties. Binary population synthesis with full stellar-structure and evolution simulations are computationally expensive requiring a large number of mass-transfer sequences. The recently developed binary population synthesis code POSYDON incorporates grids of MESA binary star simulations which are then interpolated to model large-scale populations of massive binaries. The traditional method of computing a high-density rectilinear grid of simulations is not scalable for higher-dimension grids, accounting for a range of metallicities, rotation, and eccentricity. We present a new active learning algorithm, psy-cris, which uses machine learning in the data-gathering process to adaptively and iteratively select targeted simulations to run, resulting in a custom, high-performance training set. We test psy-cris on a toy problem and find the resulting training sets require fewer simulations for accurate classification and regression than either regular or randomly sampled grids. We further apply psy-cris to the target problem of building a dynamic grid of MESA simulations, and we demonstrate that, even without fine tuning, a simulation set of only $\sim 1/4$ the size of a rectilinear grid is sufficient to achieve the same classification accuracy. We anticipate further gains when algorithmic parameters are optimized for the targeted application. We find that optimizing for classification only may lead to performance losses in regression, and vice versa. Lowering the computational cost of producing grids will enable future versions of POSYDON to cover more input parameters while preserving interpolation accuracies.

A goodness-of-fit test for one-parameter count distributions with finite second moment is proposed. The test statistic is derived from the $L_1$-distance of a function of the probability generating function of the model under the null hypothesis and that of the random variable actually generating data, when the latter belongs to a suitable wide class of alternatives. The test statistic has a rather simple form and it is asymptotically normally distributed under the null hypothesis, allowing a straightforward implementation of the test. Moreover, the test is consistent for alternative distributions belonging to the class, but also for all the alternative distributions whose probability of zero is different from that under the null hypothesis. Thus, the use of the test is proposed and investigated also for alternatives not in the class. The finite-sample properties of the test are assessed by means of an extensive simulation study.

Traditional nonparametric estimation methods often lead to a slow convergence rate in large dimensions and require unrealistically enormous sizes of datasets for reliable conclusions. We develop an approach based on mixed gradients, either observed or estimated, to effectively estimate the function at near-parametric convergence rates. The novel approach and computational algorithm could lead to methods useful to practitioners in many areas of science and engineering. Our theoretical results reveal a behavior universal to this class of nonparametric estimation problems. We explore a general setting involving tensor product spaces and build upon the smoothing spline analysis of variance (SS-ANOVA) framework. For $d$-dimensional models under full interaction, the optimal rates with gradient information on $p$ covariates are identical to those for the $(d-p)$-interaction models without gradients and, therefore, the models are immune to the "curse of interaction". For additive models, the optimal rates using gradient information are root-$n$, thus achieving the "parametric rate". We demonstrate aspects of the theoretical results through synthetic and real data applications.

Optical coherence tomography (OCT) is a micrometer-scale, volumetric imaging modality that has become a clinical standard in ophthalmology. OCT instruments image by raster-scanning a focused light spot across the retina, acquiring sequential cross-sectional images to generate volumetric data. Patient eye motion during the acquisition poses unique challenges: Non-rigid, discontinuous distortions can occur, leading to gaps in data and distorted topographic measurements. We present a new distortion model and a corresponding fully-automatic, reference-free optimization strategy for computational motion correction in orthogonally raster-scanned, retinal OCT volumes. Using a novel, domain-specific spatiotemporal parametrization of forward-warping displacements, eye motion can be corrected continuously for the first time. Parameter estimation with temporal regularization improves robustness and accuracy over previous spatial approaches. We correct each A-scan individually in 3D in a single mapping, including repeated acquisitions used in OCT angiography protocols. Specialized 3D forward image warping reduces median runtime to < 9 s, fast enough for clinical use. We present a quantitative evaluation on 18 subjects with ocular pathology and demonstrate accurate correction during microsaccades. Transverse correction is limited only by ocular tremor, whereas submicron repeatability is achieved axially (0.51 um median of medians), representing a dramatic improvement over previous work. This allows assessing longitudinal changes in focal retinal pathologies as a marker of disease progression or treatment response, and promises to enable multiple new capabilities such as supersampled/super-resolution volume reconstruction and analysis of pathological eye motion occuring in neurological diseases.

Designing learning systems which are invariant to certain data transformations is critical in machine learning. Practitioners can typically enforce a desired invariance on the trained model through the choice of a network architecture, e.g. using convolutions for translations, or using data augmentation. Yet, enforcing true invariance in the network can be difficult, and data invariances are not always known a piori. State-of-the-art methods for learning data augmentation policies require held-out data and are based on bilevel optimization problems, which are complex to solve and often computationally demanding. In this work we investigate new ways of learning invariances only from the training data. Using learnable augmentation layers built directly in the network, we demonstrate that our method is very versatile. It can incorporate any type of differentiable augmentation and be applied to a broad class of learning problems beyond computer vision. We provide empirical evidence showing that our approach is easier and faster to train than modern automatic data augmentation techniques based on bilevel optimization, while achieving comparable results. Experiments show that while the invariances transferred to a model through automatic data augmentation are limited by the model expressivity, the invariance yielded by our approach is insensitive to it by design.

This paper presents Pix2Seq, a simple and generic framework for object detection. Unlike existing approaches that explicitly integrate prior knowledge about the task, we simply cast object detection as a language modeling task conditioned on the observed pixel inputs. Object descriptions (e.g., bounding boxes and class labels) are expressed as sequences of discrete tokens, and we train a neural net to perceive the image and generate the desired sequence. Our approach is based mainly on the intuition that if a neural net knows about where and what the objects are, we just need to teach it how to read them out. Beyond the use of task-specific data augmentations, our approach makes minimal assumptions about the task, yet it achieves competitive results on the challenging COCO dataset, compared to highly specialized and well optimized detection algorithms.

Sampling methods (e.g., node-wise, layer-wise, or subgraph) has become an indispensable strategy to speed up training large-scale Graph Neural Networks (GNNs). However, existing sampling methods are mostly based on the graph structural information and ignore the dynamicity of optimization, which leads to high variance in estimating the stochastic gradients. The high variance issue can be very pronounced in extremely large graphs, where it results in slow convergence and poor generalization. In this paper, we theoretically analyze the variance of sampling methods and show that, due to the composite structure of empirical risk, the variance of any sampling method can be decomposed into \textit{embedding approximation variance} in the forward stage and \textit{stochastic gradient variance} in the backward stage that necessities mitigating both types of variance to obtain faster convergence rate. We propose a decoupled variance reduction strategy that employs (approximate) gradient information to adaptively sample nodes with minimal variance, and explicitly reduces the variance introduced by embedding approximation. We show theoretically and empirically that the proposed method, even with smaller mini-batch sizes, enjoys a faster convergence rate and entails a better generalization compared to the existing methods.