Approach For Such Models Research Articles

Assessing systematic weaknesses of DNNs using counterfactuals

With the advancement of DNNs into safety-critical applications, testing approaches for such models have gained more attention. A current direction is the search for and identification of systematic weaknesses that put safety assumptions based on average performance values at risk. Such weaknesses can take on the form of (semantically coherent) subsets or areas in the input space where a DNN performs systematically worse than its expected average. However, it is non-trivial to attribute the reason for such observed low performances to the specific semantic features that describe the subset. For instance, inhomogeneities within the data w.r.t. other (non-considered) attributes might distort results. However, taking into account all (available) attributes and their interaction is often computationally highly expensive. Inspired by counterfactual explanations, we propose an effective and computationally cheap algorithm to validate the semantic attribution of existing subsets, i.e., to check whether the identified attribute is likely to have caused the degraded performance. We demonstrate this approach on an example from the autonomous driving domain using highly annotated simulated data, where we show for a semantic segmentation model that (i) performance differences among the different pedestrian assets exist, but (ii) only in some cases is the asset type itself the reason for this reduction in the performance.

A new minimum contrast approach for inference in single-index models

Semiparametric single-index models represent an appealing compromise between parametric and nonparametric approaches and have been widely investigated in the literature. The underlying assumption in single-index models is that the information carried by the vector of covariates could be summarized by a one-dimensional projection. We propose a new, general inference approach for such models, based on a quadratic form criterion involving kernel smoothing. The approach could be applied with general single-index assumptions, in particular for mean regression models and conditional law models. The covariates could be unbounded and no trimming is necessary. A resampling method for building confidence intervals for the index parameter is proposed. Our empirical experiments reveal that the new method performs well in practice.

Inference on stochastic time-varying coefficient models

Recently, there has been considerable work on stochastic time-varying coefficient models as vehicles for modelling structural change in the macroeconomy with a focus on the estimation of the unobserved paths of random coefficient processes. The dominant estimation methods, in this context, are based on various filters, such as the Kalman filter, that are applicable when the models are cast in state space representations. This paper introduces a new class of autoregressive bounded processes that decompose a time series into a persistent random attractor, a time varying autoregressive component, and martingale difference errors. The paper examines, rigorously, alternative kernel based, nonparametric estimation approaches for such models and derives their basic properties. These estimators have long been studied in the context of deterministic structural change, but their use in the presence of stochastic time variation is novel. The proposed inference methods have desirable properties such as consistency and asymptotic normality and allow a tractable studentization. In extensive Monte Carlo and empirical studies, we find that the methods exhibit very good small sample properties and can shed light on important empirical issues such as the evolution of inflation persistence and the purchasing power parity (PPP) hypothesis.

State-space likelihoods for nonlinear fisheries time-series

State-space models are commonly used to incorporate process and observation errors in analysis of fisheries time series. A gap in analysis methods has been the lack of classical likelihood methods for nonlinear state-space models. We evaluate a method that uses weighted kernel density estimates of Bayesian posterior samples to estimate likelihoods (Monte Carlo Kernel Likelihoods, MCKL). Classical likelihoods require integration over the state-space, and we compare MCKL to the widely used errors-in-variables (EV) method, which estimates states jointly with parameters by maximizing a nonintegrated likelihood. For a simulated, linear, autoregressive model and a Schaefer model fit to cape hake (Merluccius capensis × M. paradoxus) data, classical likelihoods outperform EV likelihoods, which give asymptotically biased parameter estimates and inaccurate confidence regions. Our results on the importance of integrated state-space likelihoods also support the value of Bayesian analysis with Monte Carlo posterior integration. Both approaches provide valuable insights and can be used complementarily. Previously, Bayesian analysis was the only option for incorporating process and observation errors with complex nonlinear models. The MCKL method provides a classical approach for such models, so that choice of analysis approach need not depend on model complexity.

Economic manufacturing quantity in a just-in-time delivery system

A just-in-time (JIT) buyer demands frequent deliveries of small lots of certain products. However, there is a perception among the suppliers that participation in a JIT delivery system is economically disadvantageous for them. To test this conjecture, a generalized inventory model is developed for a supplier who has to meet a deterministic demand at fixed intervals. The generalized total cost model developed here is found to be a piecewise convex function. A simple algorithm is developed to compute the optimal batch size. When production uptime and cycle time are each equal to an integer multiple of the shipment interval, a perfect matching of shipment size occurs, and for such a situation, the generalized model specializes to more traditional inventory models. The solution approach for such models becomes much easier. It is found that, under certain conditions, the total cost decreases linearly with reduced shipment size and the suppliers benefit from this. Economic impact of ordering and setup costs red...