A variational approach to stable principal component pursuit

We introduce a new convex formulation for stable principal component pursuit (SPCP) to decompose noisy signals into low-rank and sparse representations. For numerical solutions of our SPCP formulation, we first develop a convex variational framework and then accelerate it with quasi-Newton methods. We show, via synthetic and real data experiments, that our approach offers advantages over the classical SPCP formulations in scalability and practical parameter selection.Comment: 10 pages, 5 figure

Crowd Counting with Decomposed Uncertainty

Research in neural networks in the field of computer vision has achieved remarkable accuracy for point estimation. However, the uncertainty in the estimation is rarely addressed. Uncertainty quantification accompanied by point estimation can lead to a more informed decision, and even improve the prediction quality. In this work, we focus on uncertainty estimation in the domain of crowd counting. With increasing occurrences of heavily crowded events such as political rallies, protests, concerts, etc., automated crowd analysis is becoming an increasingly crucial task. The stakes can be very high in many of these real-world applications. We propose a scalable neural network framework with quantification of decomposed uncertainty using a bootstrap ensemble. We demonstrate that the proposed uncertainty quantification method provides additional insight to the crowd counting problem and is simple to implement. We also show that our proposed method exhibits the state of the art performances in many benchmark crowd counting datasets.Comment: Accepted in AAAI 2020 (Main Technical Track

Diffusion of directed polymers in a strong random environment

We consider a system of random walks or directed polymers interacting with an environment which is random in space and time. It was shown by Imbrie and Spencer that in spatial dimensions three or above the behavior is diffusive if the directed polymer interacts weakly with the environment and if the random environment follows the Bernoulli distribution. Under the same assumption on the random environment as that of Imbrie and Spencer, we establish that in spatial dimensions four or above the behavior is still diffusive even when the directed polymer interacts strongly with the environment. More generally, we can prove that, if the random environment is bounded and if the supremum of the support of the distribution has a positive mass, then there is an integer d 0 such that in dimensions higher than d 0 the behavior of the random polymer is always diffusive.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45169/1/10955_2005_Article_BF02183745.pd

Green Investment under Policy Uncertainty and Bayesian Learning

Many countries have introduced support schemes to accelerate investments in renewable energy (RE). Experience shows that, over time, retraction or revision of support schemes become more likely. Investors in RE are greatly affected by the risk of such subsidy changes. This paper examines how investment behavior is affected by updating a subjective belief on the timing of a subsidy revision, incorporating Bayesian learning into a real options modeling approach. We analyze a scenario where a retroactive downward adjustment of fixed feed-in tariffs (FIT) is expected through a regime switching model. We find that investors are less likely to invest when the arrival rate of a policy change increases. Further, investors prefer a lower FIT with a long expected lifespan. We also consider an extension where, after retraction, electricity is sold in a free market. We find that if policy uncertainty is high, an increase in the FIT will be less effective at accelerating investment. However, if policy risk is low, FIT schemes can significantly accelerate investment, even in highly volatile markets