The Expression Problem, Gracefully

The “Expression Problem” was brought to prominence by Wadler in 1998. It is widely regarded as illustrating that the two mainstream approaches to data abstraction — procedural abstraction and type abstraction— are complementary, with the strengths of one being the weaknesses of the other. Despite an extensive literature, the origin of the problem remains ill-understood. I show that the core problem is in fact the use of global constants, and demonstrate that an important aspect of the problem goes away when Java is replaced by a language like Grace, which eliminates them

Failures in power-combining arrays

We derive a simple formula for the change in output when a device fails in a power-combining structure with identical matched devices. The loss is written in terms of the scattering coefficient of the failed device and reflection coefficient of an input port in the combining network. We apply this formula to several power combiners, including arrays in free space and enclosed waveguide structures. Our simulations indicate the output power degrades gracefully as devices fail, which is in agreement with previously published results

Recover Subjective Quality Scores from Noisy Measurements

Simple quality metrics such as PSNR are known to not correlate well with subjective quality when tested across a wide spectrum of video content or quality regime. Recently, efforts have been made in designing objective quality metrics trained on subjective data (e.g. VMAF), demonstrating better correlation with video quality perceived by human. Clearly, the accuracy of such a metric heavily depends on the quality of the subjective data that it is trained on. In this paper, we propose a new approach to recover subjective quality scores from noisy raw measurements, using maximum likelihood estimation, by jointly estimating the subjective quality of impaired videos, the bias and consistency of test subjects, and the ambiguity of video contents all together. We also derive closed-from expression for the confidence interval of each estimate. Compared to previous methods which partially exploit the subjective information, our approach is able to exploit the information in full, yielding tighter confidence interval and better handling of outliers without the need for z-scoring or subject rejection. It also handles missing data more gracefully. Finally, as side information, it provides interesting insights on the test subjects and video contents.Comment: 16 pages; abridged version appeared in Data Compression Conference (DCC) 201

Competitive Gradient Descent

We introduce a new algorithm for the numerical computation of Nash equilibria of competitive two-player games. Our method is a natural generalization of gradient descent to the two-player setting where the update is given by the Nash equilibrium of a regularized bilinear local approximation of the underlying game. It avoids oscillatory and divergent behaviors seen in alternating gradient descent. Using numerical experiments and rigorous analysis, we provide a detailed comparison to methods based on \emph{optimism} and \emph{consensus} and show that our method avoids making any unnecessary changes to the gradient dynamics while achieving exponential (local) convergence for (locally) convex-concave zero sum games. Convergence and stability properties of our method are robust to strong interactions between the players, without adapting the stepsize, which is not the case with previous methods. In our numerical experiments on non-convex-concave problems, existing methods are prone to divergence and instability due to their sensitivity to interactions among the players, whereas we never observe divergence of our algorithm. The ability to choose larger stepsizes furthermore allows our algorithm to achieve faster convergence, as measured by the number of model evaluations.Comment: Appeared in NeurIPS 2019. This version corrects an error in theorem 2.2. Source code used for the numerical experiments can be found under http://github.com/f-t-s/CGD. A high-level overview of this work can be found under http://f-t-s.github.io/projects/cgd

Monotonically improving approximate answers to relational algebra queries

We present here a query processing method that produces approximate answers to queries posed in standard relational algebra. This method is monotone in the sense that the accuracy of the approximate result improves with the amount of time spent producing the result. This strategy enables us to trade the time to produce the result for the accuracy of the result. An approximate relational model that characterizes appromimate relations and a partial order for comparing them is developed. Relational operators which operate on and return approximate relations are defined