Inverse Optimization: Closed-form Solutions, Geometry and Goodness of fit

In classical inverse linear optimization, one assumes a given solution is a candidate to be optimal. Real data is imperfect and noisy, so there is no guarantee this assumption is satisfied. Inspired by regression, this paper presents a unified framework for cost function estimation in linear optimization comprising a general inverse optimization model and a corresponding goodness-of-fit metric. Although our inverse optimization model is nonconvex, we derive a closed-form solution and present the geometric intuition. Our goodness-of-fit metric, $\rho$, the coefficient of complementarity, has similar properties to $R^2$ from regression and is quasiconvex in the input data, leading to an intuitive geometric interpretation. While $\rho$ is computable in polynomial-time, we derive a lower bound that possesses the same properties, is tight for several important model variations, and is even easier to compute. We demonstrate the application of our framework for model estimation and evaluation in production planning and cancer therapy

Poly[[diaqua­tris­(μ2-3-methyl­pyridine-2-carboxyl­ato)(3-methyl­pyridine-2-car­boxyl­ato)sodiumterbium(III)] ethanol monosolvate monohydrate]

In the title compound, {[NaTb(C7H6NO2)4(H2O)2]·C2H5OH·H2O}n, the TbIII atom is eight-coordinated in a slightly distorted square-anti­prismatic geometry defined by four carboxyl­ate O atoms and four pyridine N atoms. The bond lengths lie within the range 2.3000 (2)–2.326 (2) Å for the Tb—O bonds and 2.543 (3)–2.553 (3) Å for the Tb—N bonds. The NaI atom is five-coordinated by two water O atoms and three carboxyl­ate O atoms in a distorted square-pyramidal geometry. In the crystal, inter­molecular O—H⋯O hydrogen bonds link the mol­ecules into a three-dimensional network

Approximate Submodularity and Its Implications in Discrete Optimization

Submodularity, a discrete analog of convexity, is a key property in discrete optimization that features in the construction of valid inequalities and analysis of the greedy algorithm. In this paper, we broaden the approximate submodularity literature, which so far has largely focused on variants of greedy algorithms and iterative approaches. We define metrics that quantify approximate submodularity and use these metrics to derive properties about approximate submodularity preservation and extensions of set functions. We show that previous analyses of mixed-integer sets, such as the submodular knapsack polytope, can be extended to the approximate submodularity setting. In addition, we demonstrate that greedy algorithm bounds based on our notions of approximate submodularity are competitive with those in the literature, which we illustrate using a generalization of the uncapacitated facility location problem

Maximum Activation 3D Cube Transition System for Virtual Emotion Surveillance

The concept of barrier coverage has been utilized for with various applications of surveillance, object tracking in smart cities. In barrier coverage, it is desirable to have large number of active barriers to maximize lifetime of UAV-assisted application. Because existing studies primarily focused on the formation of barriers in two-dimensional area with limited applicability, it is indispensable to extend the barrier constructions in three-dimensional area. In this letter, a cube transition barrier system using smart UAVs is designed for three-dimensional space. Then, we formally define a problem whose goal is to maximize the number of cube transition barriers by applying a two-dimensional theory to a three-dimensional spaces. To solve this problem, we propose two algorithms to return the number of barriers and evaluate their performances based on numerical simulation results

RobustSwap: A Simple yet Robust Face Swapping Model against Attribute Leakage

Face swapping aims at injecting a source image's identity (i.e., facial features) into a target image, while strictly preserving the target's attributes, which are irrelevant to identity. However, we observed that previous approaches still suffer from source attribute leakage, where the source image's attributes interfere with the target image's. In this paper, we analyze the latent space of StyleGAN and find the adequate combination of the latents geared for face swapping task. Based on the findings, we develop a simple yet robust face swapping model, RobustSwap, which is resistant to the potential source attribute leakage. Moreover, we exploit the coordination of 3DMM's implicit and explicit information as a guidance to incorporate the structure of the source image and the precise pose of the target image. Despite our method solely utilizing an image dataset without identity labels for training, our model has the capability to generate high-fidelity and temporally consistent videos. Through extensive qualitative and quantitative evaluations, we demonstrate that our method shows significant improvements compared with the previous face swapping models in synthesizing both images and videos. Project page is available at https://robustswap.github.io/Comment: 21 page