Resilient Control for Macroeconomic Models

This paper derives a macroeconomic resilient control framework that provides the optimal feedback fiscal and monetary policy responses in response to a potentially large negative external incident. We simulate the model for the U.S. under the conditions that prevailed throughout the 2020 economic crisis that occurred due to the government lockdown that was caused by the coronavirus pandemic. We develop a discrete-time soft-constrained linear-quadratic dynamic game under a worst-case design with multiple disturbances. Within this context, we introduce a resilience feedback response and compare the case where the policymakers counter in response the external incident with the case when they do not counter. This framework is especially applicable to large-scale macroeconomic tracking control models and wavelet-based control models when formulating the magnitudes of the policy changes necessary for the unemployment rate and national output variables to maintain acceptable tracking errors in the periods following a major disruption. Our policy recommendations include the maintenance of "rainy day" funds at appropriate levels of government to mitigate the effects of large adverse events.

Generalized Sparse Additive Models

We present a unified framework for estimation and analysis of generalized additive models in high dimensions. The framework defines a large class of penalized regression estimators, encompassing many existing methods. An efficient computational algorithm for this class is presented that easily scales to thousands of observations and features. We prove minimax optimal convergence bounds for this class under a weak compatibility condition. In addition, we characterize the rate of convergence when this compatibility condition is not met. Finally, we also show that the optimal penalty parameters for structure and sparsity penalties in our framework are linked, allowing cross-validation to be conducted over only a single tuning parameter. We complement our theoretical results with empirical studies comparing some existing methods within this framework.

Correcting nuisance variation using Wasserstein distance

Profiling cellular phenotypes from microscopic imaging can provide meaningful biological information resulting from various factors affecting the cells. One motivating application is drug development: morphological cell features can be captured from images, from which similarities between different drug compounds applied at different doses can be quantified. The general approach is to find a function mapping the images to an embedding space of manageable dimensionality whose geometry captures relevant features of the input images. An important known issue for such methods is separating relevant biological signal from nuisance variation. For example, the embedding vectors tend to be more correlated for cells that were cultured and imaged during the same week than for those from different weeks, despite having identical drug compounds applied in both cases. In this case, the particular batch in which a set of experiments were conducted constitutes the domain of the data; an ideal set of image embeddings should contain only the relevant biological information (e.g., drug effects). We develop a general framework for adjusting the image embeddings in order to “forget” domain-specific information while preserving relevant biological information. To achieve this, we minimize a loss function based on distances between marginal distributions (such as the Wasserstein distance) of embeddings across domains for each replicated treatment. For the dataset we present results with, the only replicated treatment happens to be the negative control treatment, for which we do not expect any treatment-induced cell morphology changes. We find that for our transformed embeddings (i) the underlying geometric structure is not only preserved but the embeddings also carry improved biological signal; and (ii) less domain-specific information is present.

Design of adaptive backstepping congestion controller for TCP networks with UDP flows based on minimax

The congestion control problem of TCP network systems with user datagram protocol (UDP) flows is investigated in this paper. A nonlinear TCP network model with strict-feedback structure is first established. The unknown UDP flow is regarded as the external disturbance, and the maximum UDP flow is calculated by using the minimax approach. And then, a congestion control algorithm is proposed by using the adaptive backstepping approach. Meanwhile, the adaptive law is employed to estimate the unknown link capacity. The design of the adaptive law is to introduce a parameter mapping mechanism to limit the parameter identification range to a specified interval, thereby improving the estimation efficiency of the parameters. Furthermore, a state-feedback congestion controller is presented to make sure that the output of the system tracks the desired queue. The simulation results show the superiority and feasibility of the proposed method.