In this paper, we study a structured signal detection problem in Ferromagnetic Ising models with examples encompassing Ising Models on lattices, and Mean-Field type Ising Models such as dense Erdős-Rényi, and dense random regular graphs. We provide sharp constants of detection in each of these cases and thereby pinpoint an asymptotically precise relationship between the detection problem with the underlying dependence. To obtain this sharp characterization of the detection boundary at the level of sharp multiplicative constants, we derive necessary moderate deviation bounds for partial summands of magnetizations which might be of independent interest. Finally, we demonstrate how our tests can be designed to be adaptive over the strength of dependence present in the respective models.

In this paper we consider the uniformity testing problem for high-dimensional discrete distributions (multinomials) under sparse alternatives. Specifically, we derive sharp detection thresholds for testing, based on n samples, whether a discrete distribution supported on d elements differs from the uniform distribution in at most s (out of the d) coordinates and is $\varepsilon $ -far (in total variation distance) from uniformity. Our results reveal various interesting phase transitions which depend on the interplay of the sample size n and the signal strength $\varepsilon $ with the dimension d and the sparsity level s. For instance, if the sample size is less than a threshold (which depends on d and s), then all tests are asymptotically powerless, irrespective of the magnitude of the signal strength. On the other hand, if the sample size is above the threshold, then the detection boundary undergoes a further phase transition depending on the signal strength. Here, a $\chi ^{2}$ -type test attains the detection boundary in the dense regime, whereas in the sparse regime a Bonferroni correction of two maximum-type tests and a version of the Higher Criticism test is optimal up to sharp constants. These results combined provide a complete description of the phase diagram for the sparse uniformity testing problem across all regimes of the parameters n, d, s, and $\varepsilon $ . One of the challenges in dealing with multinomials is that the parameters are always constrained to lie in the simplex. This results in a layered phase transition phenomenon in the parameter space. Specifically, there is a critical sample complexity (depending only on d) below which all tests are asymptotically powerless irrespective of the signal strength and above which there is a critical threshold for the signal strength that determines testability.

In this paper, we consider asymptotically exact support recovery in the context of high dimensional and sparse Canonical Correlation Analysis (CCA). Our main results describe four regimes of interest based on information theoretic and computational considerations. In regimes of “low” sparsity we describe a simple, general, and computationally easy method for support recovery, whereas in a regime of “high” sparsity, it turns out that support recovery is information theoretically impossible. For the sake of information theoretic lower bounds, our results also demonstrate a non-trivial requirement on the “minimal” size of the nonzero elements of the canonical vectors that is required for asymptotically consistent support recovery. Subsequently, the regime of “moderate” sparsity is further divided into two sub-regimes. In the lower of the two sparsity regimes, we show that polynomial time support recovery is possible by using a sharp analysis of a co-ordinate thresholding [1] type method. In contrast, in the higher end of the moderate sparsity regime, appealing to the “Low Degree Polynomial” Conjecture [2], we provide evidence that polynomial time support recovery methods are inconsistent. Finally, we carry out numerical experiments to compare the efficacy of various methods discussed.

Recently, there have been several efforts to develop compilers that synthesize applications written in high-level languages such as C into hardware. Streaming applications form an important class of systems that need to be mapped onto hardware. In this paper we present the modeling of stream and frame based applications in C and extend a behavioral synthesis tool framework to synthesize RTL models from streaming system descriptions in C. Individual C functions get synthesized onto individual IP blocks in the synthesis framework. We describe how the behavioral synthesis tool automatically infers ports and generates the required handshaking signals for interfacing the IP blocks in the system. We describe a system level approach for interfacing synthesized IP blocks. Results of the system level synthesis and simulation are reported for Xilinx VirtexII FPGAs for single IP systems for streaming data and frame-based data, and for multiple IP systems having streaming and frame-based data.

Causal weighted quantile treatment effects (WQTEs) complement standard mean-focused causal contrasts when interest lies at the tails of the counterfactual distribution. However, existing methods for estimating and inferring causal WQTEs assume complete data on all relevant factors, which is often not the case in practice, particularly when the data are not collected for research purposes, such as electronic health records (EHRs) and disease registries. Furthermore, these data may be particularly susceptible to the outcome data being missing-not-at-random (MNAR). This paper proposes to use double sampling, through which the otherwise missing data are ascertained on a sub-sample of study units, as a strategy to mitigate bias due to MNAR data in estimating causal WQTEs. With the additional data, we present identifying conditions that do not require missingness assumptions in the original data. We then propose a novel inverse-probability weighted estimator and derive its asymptotic properties, both pointwise at specific quantiles and uniformly across quantiles over some compact subset of (0,1), allowing the propensity score and double-sampling probabilities to be estimated. For practical inference, we develop a bootstrap method that can be used for both pointwise and uniform inference. A simulation study is conducted to examine the finite sample performance of the proposed estimators. We illustrate the proposed method using EHR data examining the relative effects of 2 bariatric surgery procedures on BMI loss 3 years post-surgery.