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Personalized pricing analytics is becoming an essential tool in retailing. Upon observing the personalized information of each arriving customer, the firm needs to set a price accordingly based on the covariates such as income, education…
As an important problem in causal inference, we discuss the estimation of treatment effects (TEs). Representing the confounder as a latent variable, we propose Intact-VAE, a new variant of variational autoencoder (VAE), motivated by the…
We establish several closed pricing formula for various path-independent payoffs, under an exponential L\'evy model driven by the Variance Gamma process. These formulas take the form of quickly convergent series and are obtained via tools…
Increasing penetrations of electric vehicles (EVs) presents a large source of flexibility, which can be used to assist balancing the power grid. The flexibility of an individual EV can be quantified as a convex polytope and the flexibility…
The electric vehicle (EV) charging demands (CD) are jointly determined by the EV owners' behavior (i.e., human factor) and the electricity prices (i.e., decisions of distribution system operators (DSO)). However, most existing studies…
Learning precise representations of users and items to fit observed interaction data is the fundamental task of collaborative filtering. Existing studies usually infer entangled representations to fit such interaction data, neglecting to…
We complete the characterization of the computational complexity of equilibrium in public goods games on graphs. In this model, each vertex represents an agent deciding whether to produce a public good, with utility defined by a…
Our goal is to analyze the system of Hamilton-Jacobi-Bellman equations arising in derivative securities pricing models. The European style of an option price is constructed as a difference of the certainty equivalents to the value functions…
The conformal formulation provides a method for constructing and parametrizing solutions of the Einstein constraint equations by mapping freely chosen sets of conformal data to solutions, provided a certain set of coupled, elliptic…
Variational principles in mechanics, field theory and geometric analysis are usually formulated on closed admissible classes, where boundary variations are either fixed or independently cancelled through natural boundary conditions.…
The enterprise value (EV) is a crucial metric in company valuation as it encompasses not only equity but also assets and liabilities, offering a comprehensive measure of total value, especially for companies with diverse capital structures.…
Time-varying pricing tariffs incentivize consumers to shift their electricity demand and reduce costs, but may increase the energy burden for consumers with limited response capability. The utility must thus balance affordability and…
In recent years, Variational Autoencoders (VAEs) have been shown to be highly effective in both standard collaborative filtering applications and extensions such as incorporation of implicit feedback. We extend VAEs to collaborative…
Despite the great promise of Transformers in many sequence modeling tasks (e.g., machine translation), their deterministic nature hinders them from generalizing to high entropy tasks such as dialogue response generation. Previous work…
This paper introduces a novel approach Counterfactual Shapley Values (CSV), which enhances explainability in reinforcement learning (RL) by integrating counterfactual analysis with Shapley Values. The approach aims to quantify and compare…
Variational auto-encoders are powerful probabilistic models in generative tasks but suffer from generating low-quality samples which are caused by the holes in the prior. We propose the Coupled Variational Auto-Encoder (C-VAE), which…
This work develops problem statements related to encoders and autoencoders with the goal of elucidating variational formulations and establishing clear connections to information-theoretic concepts. Specifically, four problems with varying…
This paper introduces Concurrent Valuation Algebras (CVAs), a novel extension of ordered valuation algebras (OVAs). CVAs include two combine operators representing parallel and sequential products, adhering to a weak exchange law. This…
In this paper, we establish multiple closed-form solutions for all the variables in the Lucas-Uzawa model with externalities for the case with no parameter restrictions as well as for cases with specific parameter restrictions. These…
A set of curves or images of similar shape is an increasingly common functional data set collected in the sciences. Principal Component Analysis (PCA) is the most widely used technique to decompose variation in functional data. However, the…