A Random Attention Model

This paper illustrates how one can deduce preference from observed choices when attention is not only limited but also random. In contrast to earlier approaches, we introduce a Random Attention Model (RAM) where we abstain from any particular attention formation, and instead consider a large class of nonparametric random attention rules. Our model imposes one intuitive condition, termed Monotonic Attention, which captures the idea that each consideration set competes for the decision-maker's attention. We then develop revealed preference theory within RAM and obtain precise testable implications for observable choice probabilities. Based on these theoretical findings, we propose econometric methods for identification, estimation, and inference of the decision maker's preferences. To illustrate the applicability of our results and their concrete empirical content in specific settings, we also develop revealed preference theory and accompanying econometric methods under additional nonparametric assumptions on the consideration set for binary choice problems. Finally, we provide general purpose software implementation of our estimation and inference results, and showcase their performance using simulations

High Quality Image Interpolation via Local Autoregressive and Nonlocal 3-D Sparse Regularization

In this paper, we propose a novel image interpolation algorithm, which is formulated via combining both the local autoregressive (AR) model and the nonlocal adaptive 3-D sparse model as regularized constraints under the regularization framework. Estimating the high-resolution image by the local AR regularization is different from these conventional AR models, which weighted calculates the interpolation coefficients without considering the rough structural similarity between the low-resolution (LR) and high-resolution (HR) images. Then the nonlocal adaptive 3-D sparse model is formulated to regularize the interpolated HR image, which provides a way to modify these pixels with the problem of numerical stability caused by AR model. In addition, a new Split-Bregman based iterative algorithm is developed to solve the above optimization problem iteratively. Experiment results demonstrate that the proposed algorithm achieves significant performance improvements over the traditional algorithms in terms of both objective quality and visual perceptionComment: 4 pages, 5 figures, 2 tables, to be published at IEEE Visual Communications and Image Processing (VCIP) 201

Fair Adaptive Experiments

Randomized experiments have been the gold standard for assessing the effectiveness of a treatment or policy. The classical complete randomization approach assigns treatments based on a prespecified probability and may lead to inefficient use of data. Adaptive experiments improve upon complete randomization by sequentially learning and updating treatment assignment probabilities. However, their application can also raise fairness and equity concerns, as assignment probabilities may vary drastically across groups of participants. Furthermore, when treatment is expected to be extremely beneficial to certain groups of participants, it is more appropriate to expose many of these participants to favorable treatment. In response to these challenges, we propose a fair adaptive experiment strategy that simultaneously enhances data use efficiency, achieves an envy-free treatment assignment guarantee, and improves the overall welfare of participants. An important feature of our proposed strategy is that we do not impose parametric modeling assumptions on the outcome variables, making it more versatile and applicable to a wider array of applications. Through our theoretical investigation, we characterize the convergence rate of the estimated treatment effects and the associated standard deviations at the group level and further prove that our adaptive treatment assignment algorithm, despite not having a closed-form expression, approaches the optimal allocation rule asymptotically. Our proof strategy takes into account the fact that the allocation decisions in our design depend on sequentially accumulated data, which poses a significant challenge in characterizing the properties and conducting statistical inference of our method. We further provide simulation evidence to showcase the performance of our fair adaptive experiment strategy

Two-Step Estimation and Inference with Possibly Many Included Covariates

We study the implications of including many covariates in a first-step estimate entering a two-step estimation procedure. We find that a first order bias emerges when the number of \textit{included} covariates is "large" relative to the square-root of sample size, rendering standard inference procedures invalid. We show that the jackknife is able to estimate this "many covariates" bias consistently, thereby delivering a new automatic bias-corrected two-step point estimator. The jackknife also consistently estimates the standard error of the original two-step point estimator. For inference, we develop a valid post-bias-correction bootstrap approximation that accounts for the additional variability introduced by the jackknife bias-correction. We find that the jackknife bias-corrected point estimator and the bootstrap post-bias-correction inference perform excellent in simulations, offering important improvements over conventional two-step point estimators and inference procedures, which are not robust to including many covariates. We apply our results to an array of distinct treatment effect, policy evaluation, and other applied microeconomics settings. In particular, we discuss production function and marginal treatment effect estimation in detail

lpdensity: Local Polynomial Density Estimation and Inference

Density estimation and inference methods are widely used in empirical work. When the underlying distribution has compact support, conventional kernel-based density estimators are no longer consistent near or at the boundary because of their well-known boundary bias. Alternative smoothing methods are available to handle boundary points in density estimation, but they all require additional tuning parameter choices or other typically ad hoc modifications depending on the evaluation point and/or approach considered. This article discusses the R and Stata package lpdensity implementing a novel local polynomial density estimator proposed and studied in Cattaneo, Jansson, and Ma (2020, 2021), which is boundary adaptive and involves only one tuning parameter. The methods implemented also cover local polynomial estimation of the cumulative distribution function and density derivatives. In addition to point estimation and graphical procedures, the package offers consistent variance estimators, mean squared error optimal bandwidth selection, robust bias-corrected inference, and confidence bands construction, among other features. A comparison with other density estimation packages available in R using a Monte Carlo experiment is provided

New uniqueness results for boundary value problem of fractional differential equation

In this paper, uniqueness results for boundary value problem of fractional differential equation are obtained. Both the Banach's contraction mapping principle and the theory of linear operator are used, and a comparison between the obtained results is provided

Attention Overload

We introduce an Attention Overload Model that captures the idea that alternatives compete for the decision maker's attention, and hence the attention frequency each alternative receives decreases as the choice problem becomes larger. Using this nonparametric restriction on the random attention formation, we show that a fruitful revealed preference theory can be developed, and provide testable implications on the observed choice behavior that can be used to partially identify the decision maker's preference. Furthermore, we provide novel partial identification results on the underlying attention frequency, thereby offering the first nonparametric identification result of (a feature of) the random attention formation mechanism in the literature. Building on our partial identification results, for both preferences and attention frequency, we develop econometric methods for estimation and inference. Importantly, our econometric procedures remain valid even in settings with large number of alternatives and choice problems, an important feature of the economic environment we consider. We also provide a software package in R implementing our empirical methods, and illustrate them in a simulation study

Adjacent Slice Feature Guided 2.5D Network for Pulmonary Nodule Segmentation

More and more attention has been paid to the segmentation of pulmonary nodules. Among the current methods based on deep learning, 3D segmentation methods directly input 3D images, which takes up a lot of memory and brings huge computation. However, most of the 2D segmentation methods with less parameters and calculation have the problem of lacking spatial relations between slices, resulting in poor segmentation performance. In order to solve these problems, we propose an adjacent slice feature guided 2.5D network. In this paper, we design an adjacent slice feature fusion model to introduce information from adjacent slices. To further improve the model performance, we construct a multi-scale fusion module to capture more context information, in addition, we design an edge-constrained loss function to optimize the segmentation results in the edge region. Fully experiments show that our method performs better than other existing methods in pulmonary nodule segmentation task