Regularization is one of the most fundamental topics in optimization, statistics and machine learning. To get sparsity in estimating a parameter $u\in\mathbb{R}^d$, an $\ell_q$ penalty term, $\Vert u\Vert_q$, is usually added to the objective function. What is the probabilistic distribution corresponding to such $\ell_q$ penalty? What is the \emph{correct} stochastic process corresponding to $\Vert u\Vert_q$ when we model functions $u\in L^q$? This is important for statistically modeling high-dimensional objects such as images, with penalty to preserve certainty properties, e.g. edges in the image. In this work, we generalize the $q$-exponential distribution (with density proportional to) $\exp{(- \frac{1}{2}|u|^q)}$ to a stochastic process named \emph{$Q$-exponential (Q-EP) process} that corresponds to the $L_q$ regularization of functions. The key step is to specify consistent multivariate $q$-exponential distributions by choosing from a large family of elliptic contour distributions. The work is closely related to Besov process which is usually defined in terms of series. Q-EP can be regarded as a definition of Besov process with explicit probabilistic formulation, direct control on the correlation strength, and tractable prediction formula. From the Bayesian perspective, Q-EP provides a flexible prior on functions with sharper penalty ($q<2$) than the commonly used Gaussian process (GP, $q=2$). We compare GP, Besov and Q-EP in modeling functional data, reconstructing images and solving inverse problems and demonstrate the advantage of our proposed methodology.

We jointly analyzed 23 L-band ALOS PALSAR scenes and over 200 soil core samples collected near the Toolik region. Based on the fact that the maximum thaw subsidence is proportional to the total soil water content in the active layer, we derived an equivalent water depth map over the Toolik area using the InSAR thaw subsidence estimates. We quantified the noise terms in the InSAR measurements and demonstrated that the DEM error is the dominant error source in the study area, mostly in steep terrains. We developed a mitigation strategy that reduces the uncertainty in the InSAR-based soil water estimates from$> 20\text{cm}$to$< 10\text{cm}$. Our study suggests that InSAR has greater observational capabilities than previously assumed for monitoring the active layer soil water storage above continuous permafrost.

The growing application of DL makes detecting and fixing defective DL programs of paramount importance. Recent studies on DL defects report that TensorFlow API misuses represent a common class of DL defects. However to effectively detect, fix, and verify them remains an understudied problem. This paper presents the TensorFlow API misuses Detector And Fixer (TADAF) technique, which relies on 11 common API misuses patterns and corresponding fixes that we extracted from StackOverftow. TADAF statically analyses a TensorFlow program for identifying matches of any of the 11 patterns. If it finds a match, it automatically generates a fixed version of the program. To verify that the misuse brings a tangible negative effect, TADAF reports functional, accuracy, or efficiency differences when training and testing (with the same data) the original and fixed versions of the program. Our preliminary evaluation on five GitHub projects shows that TADAF detected and fixed all the API misuses.

Here we jointly analyzed L-band ALOS PALSAR data and more than 200 soil samples in order to determine soil properties that control the seasonal freeze-thaw process of the active layer. We found that the magnitude of the seasonal freeze-thaw (FT) deformation strongly correlates with land vegetation cover types. This is because the seasonal FT deformation is a direct measure of the active layer soil water content, and the amount of water in the soil limits the type of vegetation that can grow. Furthermore, we found that soil carbon amount also correlates with land cover types. Soils that contain more carbon in the active layer also tend to produce larger seasonal FT deformation. Our results suggest that there are many previously unrecognized ways that InSAR can be used for monitoring changes in hydrological and ecological characteristics in soils above continuous permafrost.