A Moment-Matching Approach to Testable Learning and a New Characterization of Rademacher Complexity

A remarkable recent paper by Rubinfeld and Vasilyan (2022) initiated the study of \emph{testable learning}, where the goal is to replace hard-to-verify distributional assumptions (such as Gaussianity) with efficiently testable ones and to require that the learner succeed whenever the unknown distribution passes the corresponding test. In this model, they gave an efficient algorithm for learning halfspaces under testable assumptions that are provably satisfied by Gaussians. In this paper we give a powerful new approach for developing algorithms for testable learning using tools from moment matching and metric distances in probability. We obtain efficient testable learners for any concept class that admits low-degree \emph{sandwiching polynomials}, capturing most important examples for which we have ordinary agnostic learners. We recover the results of Rubinfeld and Vasilyan as a corollary of our techniques while achieving improved, near-optimal sample complexity bounds for a broad range of concept classes and distributions. Surprisingly, we show that the information-theoretic sample complexity of testable learning is tightly characterized by the Rademacher complexity of the concept class, one of the most well-studied measures in statistical learning theory. In particular, uniform convergence is necessary and sufficient for testable learning. This leads to a fundamental separation from (ordinary) distribution-specific agnostic learning, where uniform convergence is sufficient but not necessary.Comment: 34 page

CFD simulations on the effect of catalysts on the hydrodeoxygenation of bio-oil

Bio-oil derived from lignocellulose biomass is an emerging alternative resource to conventional fossil fuel. However, the as-obtained unprocessed bio oil is oxy-rich, has low pH and contains high moisture, which suppresses the heating value; thus, its mixing with conventional fuel is not compatible. Therefore, studies on the upgradation of bio oil using catalytic hydrodeoxygenation (HDO) have become prominent in recent years. This study presents computational fluid dynamics (CFD) based simulation results on the effect of catalysts (Pt/Al2O3, Ni–Mo/Al2O3, Co–Mo/Al2O3) on the upgradation of bio oil using a hydrodeoxygenation process in an ebullated bed reactor. These numerical simulations are performed using an Eulerian multiphase flow module that is available in a commercial CFD based solver, ANSYS Fluent 14.5. Prior to obtaining the new results, the present numerical solution methodology is validated by reproducing some of the experimental results on the upgradation of bio oil available in the literature. Furthermore, the influence of weight hourly space velocities (WHSVs), operating temperature, and pressure inside the reactor for the different catalysts on the performance of HDO for bio oil upgradation in an ebullated bed reactor are delineated. It is observed that the gaseous stream products are higher in the presence of Pt/Al2O3 catalyst; phenols are higher when Ni–Mo/Al2O3 is used, and higher aromatics are obtained with the Co–Mo/Al2O3 catalyst. Finally, a comparison among the mass fraction of the individual species of three phases with respect to different catalysts for various combinations of WHSV, temperature and pressure values are presented