We study an online learning problem subject to the constraint of individual fairness, which requires that similar individuals are treated similarly. Unlike prior work on individual fairness, we do not assume the similarity measure among individuals is known, nor do we assume that such measure takes a certain parametric form.

Currently, they are often characterized via intensity function which limits model's expressiveness due to unrealistic assumptions on

Given CRF potentials, one can write down the marginal predictions after only passing the initial messages from factors to variables. This paper incorporates that parametric form into a neural network, and fits it directly to minimize training error. This architecture appears to be empirically successful on a meaningful benchmark. I found the framing of the work partially misleading: As far as I can tell, the cost function reported doesn't care about structured prediction just pixel-wise errors, and no CRF model is actually fitted. To me "structured CRF prediction" means that there is a joint distribution over the labels given an input.

We study an online learning problem subject to the constraint of individual fairness, which requires that similar individuals are treated similarly. Unlike prior work on individual fairness, we do not assume the similarity measure among individuals is known, nor do we assume that such measure takes a certain parametric form. In each round, the auditor examines the learner's decisions and attempts to identify a pair of individuals that are treated unfairly by the learner. We provide a general reduction framework that reduces online classification in our model to standard online classification, which allows us to leverage existing online learning algorithms to achieve sub-linear regret and number of fairness violations. Surprisingly, in the stochastic setting where the data are drawn independently from a distribution, we are also able to establish PAC-style fairness and accuracy generalization guarantees (Rothblum and Yona (2018)), despite only having access to a very restricted form of fairness feedback.

The authors present a novel way to automatically generate the dependency structure for constructing inference network. They frame the problem as a graphical-model-inversion problem and propose to use variable elimination and the min-fill heuristic. The proposed method generates a faithful and minimal structure for constructing inference network. The authors show that the generated inference network outperforms the existing heuristically designed network and the fully connected network. I have the following questions related to this work.

Point processes are becoming very popular in modeling asynchronous sequential data due to their sound mathematical foundation and strength in modeling a variety of real-world phenomena. Currently, they are often characterized via intensity function which limits model's expressiveness due to unrealistic assumptions on its parametric form used in practice. Furthermore, they are learned via maximum likelihood approach which is prone to failure in multi-modal distributions of sequences. In this paper, we propose an intensity-free approach for point processes modeling that transforms nuisance processes to a target one. Furthermore, we train the model using a likelihood-free leveraging Wasserstein distance between point processes. Experiments on various synthetic and real-world data substantiate the superiority of the proposed point process model over conventional ones.

Bismut [1] first introduced linear backward stochastic differential equations (BSDEs in short) as the adjoint equation of the classical stochastic optimal control problem. In 1990, Pardoux and Peng firstly proved the existence and uniqueness of nonlinear BSDEs with Lipschitz condition [2]. Since then, the theory of BSDEs has been studied by many researchers and applied in a wide range of areas, such as in stochastic optimal control and mathematical finance [3, 4]. When a BSDE is coupled with a (forward) stochastic differential equation (SDE in short), the system is usually called a forward-backward stochastic differential equation (FBSDE in short). We can refer to the literatures in [5, 6, 7, 8, 9, 10] which studied the existence, uniqueness and the applications of coupled or fully-coupled FBSDEs.

Estimating the uncertainty in deep neural network predictions is crucial for many real-world applications. A common approach to model uncertainty is to choose a parametric distribution and fit the data to it using maximum likelihood estimation. The chosen parametric form can be a poor fit to the data-generating distribution, resulting in unreliable uncertainty estimates. In this work, we propose SampleNet, a flexible and scalable architecture for modeling uncertainty that avoids specifying a parametric form on the output distribution. SampleNets do so by defining an empirical distribution using samples that are learned with the Energy Score and regularized with the Sinkhorn Divergence. SampleNets are shown to be able to well-fit a wide range of distributions and to outperform baselines on large-scale real-world regression tasks.

We propose a two-phase systematical framework for approximation algorithm design and analysis via Lyapunov function. The first phase consists of using Lyapunov function as an input and outputs a continuous-time approximation algorithm with a provable approximation ratio. The second phase then converts this continuous-time algorithm to a discrete-time algorithm with almost the same approximation ratio along with provable time complexity. One distinctive feature of our framework is that we only need to know the parametric form of the Lyapunov function whose complete specification will not be decided until the end of the first phase by maximizing the approximation ratio of the continuous-time algorithm. Some immediate benefits of the Lyapunov function approach include: (i) unifying many existing algorithms; (ii) providing a guideline to design and analyze new algorithms; and (iii) offering new perspectives to potentially improve existing algorithms. We use various submodular maximization problems as running examples to illustrate our framework.

Ordinary differential equations (ODEs), commonly used to characterize the dynamic systems, are difficult to propose in closed-form for many complicated scientific applications, even with the help of domain expert. We propose a fast and accurate data-driven method, MAGI-X, to learn the unknown dynamic from the observation data in a non-parametric fashion, without the need of any domain knowledge. Unlike the existing methods that mainly rely on the costly numerical integration, MAGI-X utilizes the powerful functional approximator of neural network to learn the unknown nonlinear dynamic within the MAnifold-constrained Gaussian process Inference (MAGI) framework that completely circumvents the numerical integration. Comparing against the state-of-the-art methods on three realistic examples, MAGI-X achieves competitive accuracy in both fitting and forecasting while only taking a fraction of computational time. Moreover, MAGI-X provides practical solution for the inference of partial observed systems, which no previous method is able to handle.