Interpreting Neural Networks Using Flip Points

Neural networks have been criticized for their lack of easy interpretation, which undermines confidence in their use for important applications. Here, we introduce a novel technique, interpreting a trained neural network by investigating its flip points. A flip point is any point that lies on the boundary between two output classes: e.g. for a neural network with a binary yes/no output, a flip point is any input that generates equal scores for "yes" and "no". The flip point closest to a given input is of particular importance, and this point is the solution to a well-posed optimization problem. This paper gives an overview of the uses of flip points and how they are computed. Through results on standard datasets, we demonstrate how flip points can be used to provide detailed interpretation of the output produced by a neural network. Moreover, for a given input, flip points enable us to measure confidence in the correctness of outputs much more effectively than softmax score. They also identify influential features of the inputs, identify bias, and find changes in the input that change the output of the model. We show that distance between an input and the closest flip point identifies the most influential points in the training data. Using principal component analysis (PCA) and rank-revealing QR factorization (RR-QR), the set of directions from each training input to its closest flip point provides explanations of how a trained neural network processes an entire dataset: what features are most important for classification into a given class, which features are most responsible for particular misclassifications, how an adversary might fool the network, etc. Although we investigate flip points for neural networks, their usefulness is actually model-agnostic

Surface wave non-reciprocity via time-modulated metamaterials

We investigate how Rayleigh waves interact with time-modulated resonators located on the free surface of a semi-infinite elastic medium. We begin by studying the dynamics of a single resonator with time-modulated stiffness, we evaluate the accuracy of an analytical approximation of the resonator response and identify the parameter ranges in which its behavior remains stable. Then, we develop an analytical model to describe the interaction between surface waves and an array of resonators with spatio-temporally modulated stiffness. By combining our analytical models with full-scale numerical simulations, we demonstrate that spatio-temporal stiffness modulation of this elastic metasurface leads to the emergence of non-reciprocal features in the Rayleigh wave spectrum. Specifically, we show how the frequency content of a propagating signal can be filtered and converted when traveling through the modulated medium, and illustrate how surface-to-bulk wave conversion plays a role in these phenomena. Throughout this article, we indicate bounds of modulation parameters for which our theory is reliable, thus providing guidelines for future experimental studies on the topic

Measuring equity in household's health care payments (Tehran-Iran 2013): Technical points for health policy decision makers

Background: Households' financial protection against health payments and expenditures and equity in utilization of health care services are of the most important tasks of governments. This study aims to measuring equity in household's health care payments according to fairness in financial contribution (FFC) and Kakwani indices in Tehran-Iran, 2013. Methods: This cross-sectional study was conducted in 2014.The study sample size was estimated to be 2200 households. Households were selected using stratified-cluster sampling including typical families who reside in the city of Tehran. The data were analyzed through Excel and Stata v.11software. Recall period for the inpatient care was 1 year and for outpatient1 month. Results: The indicator of FFC for households in health financing was estimated to be 0.68 and the trend of the indicator was ascending by the rise in the ranking of households' financial level. The Kakwani index was estimated to be a negative number (-0.00125) which indicated the descending trend of health financing system. By redistribution of incomes or the exempt of the poorest quintiles from health payments, Kakwani index was estimated to be a positive number (0.090555) which indicated the ascending trend of health financing system. Conclusion: According to this study, the equity indices in health care financing denote injustice and a descending trend in the health care financing system. This finding clearly shows that deliberate policy making in health financing by national health authorities and protecting low-income households against health expenditures are required to improve the equity in health

Performance, kinetic, and biodegradation pathway evaluation of anaerobic fixed film fixed bed reactor in removing phthalic acid esters from wastewater

Emerging and hazardous environmental pollutants like phthalic acid esters (PAEs) are one of the recent concerns worldwide. PAEs are considered to have diverse endocrine disrupting effects on human health. Industrial wastewater has been reported as an important environment with high concentrations of PAEs. In the present study, four short-chain PAEs including diallyl phthalate (DAP), diethyl phthalate (DEP), dimethyl phthalate (DMP), and phthalic acid (PA) were selected as a substrate for anaerobic fixed film fixed bed reactor (AnFFFBR). The process performances of AnFFFBR, and also its kinetic behavior, were evaluated to find the best eco-friendly phthalate from the biodegradability point of view. According to the results and kinetic coefficients, removing and mineralizing of DMP occurred at a higher rate than other phthalates. In optimum conditions 92.5, 84.41, and 80.39% of DMP, COD, and TOC were removed. DAP was found as the most bio-refractory phthalate. The second-order (Grau) model was selected as the best model for describing phthalates removal