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Natural language models are often summarized through a high-dimensional set of descriptive metrics including training corpus size, training time, the number of trainable parameters, inference times, and evaluation statistics that assess performance across tasks. The high dimensional nature of these metrics yields challenges with regard to objectively comparing models; in particular it is challenging to assess the trade-off models make between performance and resources (compute time, memory, etc.). We apply Data Envelopment Analysis (DEA) to this problem of assessing the resource-performance trade-off. DEA is a nonparametric method that measures productive efficiency of abstract units that consume one or more inputs and yield at least one output. We recast natural language models as units suitable for DEA, and we show that DEA can be used to create an effective framework for quantifying model performance and efficiency. A central feature of DEA is that it identifies a subset of models that live on an efficient frontier of performance. DEA is also scalable, having been applied to problems with thousands of units. We report empirical results of DEA applied to 14 different language models that have a variety of architectures, and we show that DEA can be used to identify a subset of models that effectively balance resource demands against performance., Comment: 9 pages, 1 figure, Eval4NLP workshop

Multiple wireless sensing tasks, e.g., radar detection for driver safety, involve estimating the "channel" or relationship between signal transmitted and received. In this work, we focus on a certain channel model known as the delay-doppler channel. This model begins to be useful in the high frequency carrier setting, which is increasingly common with developments in millimeter-wave technology. Moreover, the delay-doppler model then continues to be applicable even when using signals of large bandwidth, which is a standard approach to achieving high resolution channel estimation. However, when high resolution is desirable, this standard approach results in a tension with the desire for efficiency because, in particular, it immediately implies that the signals in play live in a space of very high dimension $N$ (e.g., ~$10^6$ in some applications), as per the Shannon-Nyquist sampling theorem. To address this difficulty, we propose a novel randomized estimation scheme called Sparse Channel Estimation, or SCE for short, for channel estimation in the $k$-sparse setting (e.g., $k$ objects in radar detection). This scheme involves an estimation procedure with sampling and space complexity both on the order of $k(logN)^3$, and arithmetic complexity on the order of $k(log N)^3 + k^2$, for $N$ sufficiently large. To the best of our knowledge, Sparse Channel Estimation (SCE) is the first of its kind to achieve these complexities simultaneously -- it seems to be extremely efficient! As an added advantage, it is a simple combination of three ingredients, two of which are well-known and widely used, namely digital chirp signals and discrete Gaussian filter functions, and the third being recent developments in sparse fast fourier transform algorithms., Comment: PhD thesis, University of Wisconsin -- Madison, May 2020. Thesis advisor: Shamgar Gurevich

In this paper we study the distributions of the number of real solutions to the power flow equations over varying electrical parameters. We introduce a new monodromy and parameter homotopy continuation method for quickly finding all solutions to the power flow equations. We apply this method to find distributions of the number of real solutions to the power flow equations and compare these distributions to those of random polynomials. It is observed that while the power flow equations tend to admit many fewer real-valued solutions than a bound on the total number of complex solutions, for low levels of load they tend to admit many more than a corresponding random polynomial. We show that for cycle graphs the number of real solutions can achieve the maximum bound for specific parameter values and for complete graphs with four or more vertices there are susceptance values that give infinitely many real solutions., Comment: 13 pages