Achievable Error Exponents for Almost Fixed-Length Hypothesis Testing and Classification

We revisit multiple hypothesis testing and propose a two-phase test, where each phase is a fixed-length test and the second-phase proceeds only if a reject option is decided in the first phase. We derive achievable error exponents of error probabilities under each hypothesis and show that our two-phase test bridges over fixed-length and sequential tests in the similar spirit of Lalitha and Javidi (ISIT, 2016) for binary hypothesis testing. Specifically, our test could achieve the performance close to a sequential test with the asymptotic complexity of a fixed-length test and such test is named the almost fixed-length test. Motivated by practical applications where the generating distribution under each hypothesis is \emph{unknown}, we generalize our results to the statistical classification framework of Gutman (TIT, 1989). We first consider binary classification and then generalize our results to $M$-ary classification. For both cases, we propose a two-phase test, derive achievable error exponents and demonstrate that our two-phase test bridges over fixed-length and sequential tests. In particular, for $M$-ary classification, no final reject option is required to achieve the same exponent as the sequential test of Haghifam, Tan, and Khisti (TIT, 2021). Our results generalize the design and analysis of the almost fixed-length test for binary hypothesis testing to broader and more practical families of $M$-ary hypothesis testing and statistical classification.

Efficient Image Super-Resolution using Vast-Receptive-Field Attention

The attention mechanism plays a pivotal role in designing advanced super-resolution (SR) networks. In this work, we design an efficient SR network by improving the attention mechanism. We start from a simple pixel attention module and gradually modify it to achieve better super-resolution performance with reduced parameters. The specific approaches include: (1) increasing the receptive field of the attention branch, (2) replacing large dense convolution kernels with depth-wise separable convolutions, and (3) introducing pixel normalization. These approaches paint a clear evolutionary roadmap for the design of attention mechanisms. Based on these observations, we propose VapSR, the VAst-receptive-field Pixel attention network. Experiments demonstrate the superior performance of VapSR. VapSR outperforms the present lightweight networks with even fewer parameters. And the light version of VapSR can use only 21.68% and 28.18% parameters of IMDB and RFDN to achieve similar performances to those networks. The code and models are available at url{https://github.com/zhoumumu/VapSR.

Resolution Limits of Non-Adaptive 20 Questions Search for a Moving Target

Using the 20 questions estimation framework with query-dependent noise, we study non-adaptive search strategies for a moving target over the unit cube with unknown initial location and velocities under a piecewise constant velocity model. In this search problem, there is an oracle who knows the instantaneous location of the target at any time. Our task is to query the oracle as few times as possible to accurately estimate the location of the target at any specified time. We first study the case where the oracle's answer to each query is corrupted by discrete noise and then generalize our results to the case of additive white Gaussian noise. In our formulation, the performance criterion is the resolution, which is defined as the maximal $L_\infty$ distance between the true locations and estimated locations. We characterize the minimal resolution of an optimal non-adaptive query procedure with a finite number of queries by deriving non-asymptotic and asymptotic bounds. Our bounds are tight in the first-order asymptotic sense when the number of queries satisfies a certain condition and our bounds are tight in the stronger second-order asymptotic sense when the target moves with a constant velocity. To prove our results, we relate the current problem to channel coding, borrow ideas from finite blocklength information theory and construct bounds on the number of possible quantized target trajectories.

Asymptotics for Outlier Hypothesis Testing

We revisit the outlier hypothesis testing framework of Li \emph{et al.} (TIT 2014) and derive fundamental limits for the optimal test. In outlier hypothesis testing, one is given multiple observed sequences, where most sequences are generated i.i.d. from a nominal distribution. The task is to discern the set of outlying sequences that are generated according to anomalous distributions. The nominal and anomalous distributions are \emph{unknown}. We consider the case of multiple outliers where the number of outliers is unknown and each outlier can follow a different anomalous distribution. Under this setting, we study the tradeoff among the probabilities of misclassification error, false alarm and false reject. Specifically, we propose a threshold-based test that ensures exponential decay of misclassification error and false alarm probabilities. We study two constraints on the false reject probability, with one constraint being that it is a non-vanishing constant and the other being that it has an exponential decay rate. For both cases, we characterize bounds on the false reject probability, as a function of the threshold, for each tuple of nominal and anomalous distributions. Finally, we demonstrate the asymptotic optimality of our test under the generalized Neyman-Pearson criterion.

Resolution Limits of 20 Questions Search Strategies for Moving Targets

We establish fundamental limits of tracking a moving target over the unit cube under the framework of 20 questions with measurement-dependent noise. In this problem, there is an oracle who knows the instantaneous location of a target. Our task is to query the oracle as few times as possible to accurately estimate the trajectory of the moving target, whose initial location and velocity is \emph{unknown}. We study the case where the oracle's answer to each query is corrupted by random noise with query-dependent discrete distribution. In our formulation, the performance criterion is the resolution, which is defined as the maximal absolute value between the true location and estimated location at each discrete time during the searching process. We are interested in the minimal resolution of any non-adaptive searching procedure with a finite number of queries and derive approximations to this optimal resolution via the second-order asymptotic analysis.

Objects detection for remote sensing images based on polar coordinates

Oriented and horizontal bounding box are two typical output forms in the field of remote sensing object detection. In this filed, most present state-of-the-art detectors belong to anchor-based method and perform regression tasks in Cartesian coordinates, which cause the design of oriented detectors is much more complicated than the horizontal ones, because the former usually needs to devise more complex rotated anchors, rotated Intersection-over-Union (IOU) and rotated Non Maximum Supression (NMS). In this paper, we propose a novel anchor-free detector modeled in polar coordinates to detect objects for remote sensing images, which makes the acquisition of oriented output form be as simple as the horizontal one. Our model, named Polar Remote Sensing Object Detector (P-RSDet), takes the center point of each object as the pole point and the horizontal positive direction as the polar axis to establish the polar coordinate system. The detection of one object can be regarded as predictions of one polar radius and two polar angles for both horizontal and oriented bounding box by our model. P-RSDet realizes the combination of two output forms with minimum cost. Experiments show that our P-RSDet achieves competitive performances on DOTA, UCAS-AOD and NWPU VHR-10 datasets on both horizontal and oreinted detection fileds.

Oriented Objects as pairs of Middle Lines

The detection of oriented objects is frequently appeared in the field of natural scene text detection as well as object detection in aerial images. Traditional detectors for oriented objects are common to rotate anchors on the basis of the RCNN frameworks, which will multiple the number of anchors with a variety of angles, coupled with rotating NMS algorithm, the computational complexities of these models are greatly increased. In this paper, we propose a novel model named Oriented Objects Detection Network O^2-DNet to detect oriented objects by predicting a pair of middle lines inside each target. O^2-DNet is an one-stage, anchor-free and NMS-free model. The target line segments of our model are defined as two corresponding middle lines of original rotating bounding box annotations which can be transformed directly instead of additional manual tagging. Experiments show that our O^2-DNet achieves excellent performance on ICDAR 2015 and DOTA datasets. It is noteworthy that the objects in COCO can be regard as a special form of oriented objects with an angle of 90 degrees. O^2-DNet can still achieve competitive results in these general natural object detection datasets.

GeoSQA: A Benchmark for Scenario-based Question Answering in the Geography Domain at High School Level

Scenario-based question answering (SQA) has attracted increasing research attention. It typically requires retrieving and integrating knowledge from multiple sources, and applying general knowledge to a specific case described by a scenario. SQA widely exists in the medical, geography, and legal domains---both in practice and in the exams. In this paper, we introduce the GeoSQA dataset. It consists of 1,981 scenarios and 4,110 multiple-choice questions in the geography domain at high school level, where diagrams (e.g., maps, charts) have been manually annotated with natural language descriptions to benefit NLP research. Benchmark results on a variety of state-of-the-art methods for question answering, textual entailment, and reading comprehension demonstrate the unique challenges presented by SQA for future research.