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In this paper we develop a statistical theory and an implementation of deep learning models. We show that an elegant variable splitting scheme for the alternating direction method of multipliers optimises a deep learning objective. We allow…

Machine Learning · Statistics 2015-09-22 Nicholas G. Polson , Brandon T. Willard , Massoud Heidari

We introduce a generic class of dynamic nonlinear heterogeneous parameter models that incorporate individual and time fixed effects in both the intercept and slope. These models are subject to the incidental parameter problem, in that the…

Econometrics · Economics 2026-01-27 Xuan Leng , Jiaming Mao , Yutao Sun

We study adaptive estimation and inference in ill-posed linear inverse problems defined by conditional moment restrictions. Existing regularized estimators such as Regularized DeepIV (RDIV) require prior knowledge of the smoothness of the…

Machine Learning · Statistics 2026-03-03 Jiyuan Tan , Vasilis Syrgkanis

Deep learning models are increasingly deployed in safety-critical tasks where predictions must satisfy hard constraints, such as physical laws, fairness requirements, or safety limits. However, standard architectures lack built-in…

Machine Learning · Computer Science 2025-11-26 Gonzalo E. Constante-Flores , Hao Chen , Can Li

Classical learning theory suggests that the optimal generalization performance of a machine learning model should occur at an intermediate model complexity, with simpler models exhibiting high bias and more complex models exhibiting high…

Machine Learning · Statistics 2020-11-09 Ben Adlam , Jeffrey Pennington

This script offers an implementation-oriented introduction to deep learning methods for solving and estimating high-dimensional dynamic stochastic models in economics and finance. Its starting point is the curse of dimensionality:…

General Economics · Economics 2026-05-15 Simon Scheidegger

A key task in actuarial modelling involves modelling the distributional properties of losses. Classic (distributional) regression approaches like Generalized Linear Models (GLMs; Nelder and Wedderburn, 1972) are commonly used, but…

Machine Learning · Statistics 2024-06-04 Benjamin Avanzi , Eric Dong , Patrick J. Laub , Bernard Wong

The inferential models (IM) framework provides prior-free, frequency-calibrated, posterior probabilistic inference. The key is the use of random sets to predict unobservable auxiliary variables connected to the observable data and unknown…

Statistics Theory · Mathematics 2016-01-26 Ryan Martin , Chuanhai Liu

In performative learning, the data distribution reacts to the deployed model - for example, because strategic users adapt their features to game it - which creates a more complex dynamic than in classical supervised learning. One should…

Machine Learning · Computer Science 2025-10-15 Edwige Cyffers , Alireza Mirrokni , Marco Mondelli

While fiducial inference was widely considered a big blunder by R.A. Fisher, the goal he initially set --`inferring the uncertainty of model parameters on the basis of observations' -- has been continually pursued by many statisticians. To…

Machine Learning · Statistics 2024-08-01 Faming Liang , Sehwan Kim , Yan Sun

Bayesian inference in function space has gained attention due to its robustness against overparameterization in neural networks. However, approximating the infinite-dimensional function space introduces several challenges. In this work, we…

Machine Learning · Computer Science 2024-12-23 Sophie Steger , Christian Knoll , Bernhard Klein , Holger Fröning , Franz Pernkopf

Approximating time-varying unobserved heterogeneity by discrete types has become increasingly popular in economics. Yet, provably valid post-clustering inference for target parameters in models that do not impose an exact group structure is…

Econometrics · Economics 2025-10-20 Jad Beyhum , Martin Mugnier

Among the most critical limitations of deep learning NLP models are their lack of interpretability, and their reliance on spurious correlations. Prior work proposed various approaches to interpreting the black-box models to unveil the…

Computation and Language · Computer Science 2021-10-08 Xiaochuang Han , Yulia Tsvetkov

Obtaining valid treatment effect inference remains a challenging problem when dealing with numerous instruments and non-sparse control variables. In this paper, we propose a novel ridge regularization-based instrumental variables method for…

Econometrics · Economics 2025-10-17 Xiduo Chen , Xingdong Feng , Antonio F. Galvao , Yeheng Ge

In this paper, we present a general specification for Functional Effects Models, which use Machine Learning (ML) methodologies to learn individual-specific preference parameters from socio-demographic characteristics, therefore accounting…

Machine Learning · Statistics 2025-09-23 Nicolas Salvadé , Tim Hillel

Indirect inference requires simulating realisations of endogenous variables from the model under study. When the endogenous variables are discontinuous functions of the model parameters, the resulting indirect inference criterion function…

Economics · Quantitative Finance 2019-07-11 David T. Frazier , Tatsushi Oka , Dan Zhu

Causal influence measures for machine learnt classifiers shed light on the reasons behind classification, and aid in identifying influential input features and revealing their biases. However, such analyses involve evaluating the classifier…

Machine Learning · Computer Science 2018-04-10 Shayak Sen , Piotr Mardziel , Anupam Datta , Matthew Fredrikson

Optimal experimental design is a well studied field in applied science and engineering. Techniques for estimating such a design are commonly used within the framework of parameter estimation. Nonetheless, in recent years parameter…

Machine Learning · Statistics 2025-01-13 Md Shahriar Rahim Siddiqui , Arman Rahmim , Eldad Haber

We provide an inferential framework to assess variable importance for heterogeneous treatment effects. This assessment is especially useful in high-risk domains such as medicine, where decision makers hesitate to rely on black-box treatment…

Methodology · Statistics 2026-05-11 Pawel Morzywolek , Peter B. Gilbert , Alex Luedtke

The lack of interpretability and transparency are preventing economists from using advanced tools like neural networks in their empirical research. In this paper, we propose a class of interpretable neural network models that can achieve…

Econometrics · Economics 2020-12-01 Yucheng Yang , Zhong Zheng , Weinan E