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The use of neural networks to approximate partial differential equations (PDEs) has gained significant attention in recent years. However, the approximation of PDEs with localised phenomena, e.g., sharp gradients and singularities, remains…

Numerical Analysis · Mathematics 2025-01-30 Santiago Badia , Wei Li , Alberto F. Martín

A method is introduced for approximate marginal likelihood inference via adaptive Gaussian quadrature in mixed models with a single grouping factor. The core technical contribution is an algorithm for computing the exact gradient of the…

Methodology · Statistics 2024-11-13 Alex Stringer

In many applications we seek to maximize an expectation with respect to a distribution over discrete variables. Estimating gradients of such objectives with respect to the distribution parameters is a challenging problem. We analyze…

Machine Learning · Statistics 2019-06-18 Evgeny Andriyash , Arash Vahdat , Bill Macready

Deep neural network training involves both forward propagation (from features through logits to loss) and backward propagation (from loss through gradients to parameter updates). While perturbations along the forward chain, including…

Machine Learning · Computer Science 2026-05-29 Hua Li

Simultaneously optimizing multiple, frequently conflicting, molecular properties is a key bottleneck in the development of novel therapeutics. Although a promising approach, the efficacy of multi-task learning is often compromised by…

Machine Learning · Computer Science 2025-10-01 Mason Minot , Gisbert Schneider

Training models with discrete latent variables is challenging due to the high variance of unbiased gradient estimators. While low-variance reparameterization gradients of a continuous relaxation can provide an effective solution, a…

Machine Learning · Computer Science 2022-11-16 Zhe Dong , Andriy Mnih , George Tucker

Latent variable models have been widely applied in different fields of research in which the constructs of interest are not directly observable, so that one or more latent variables are required to reduce the complexity of the data. In…

Statistics Theory · Mathematics 2014-07-07 Silvia Bianconcini

Marginal maximum likelihood estimation (MMLE) in item response theory (IRT) is highly sensitive to aberrant responses, such as careless answering and random guessing, which can reduce estimation accuracy. To address this issue, this study…

Methodology · Statistics 2025-02-18 Yuki Itaya , Kenichi Hayashi

Estimators derived from a divergence criterion such as $\varphi-$divergences are generally more robust than the maximum likelihood ones. We are interested in particular in the so-called MD$\varphi$DE, an estimator built using a dual…

Computation · Statistics 2016-06-14 Diaa Al Mohamad , Michel Broniatowski

Attribution algorithms are frequently employed to explain the decisions of neural network models. Integrated Gradients (IG) is an influential attribution method due to its strong axiomatic foundation. The algorithm is based on integrating…

Machine Learning · Computer Science 2023-12-19 Chase Walker , Sumit Jha , Kenny Chen , Rickard Ewetz

Gradient estimation -- approximating the gradient of an expectation with respect to the parameters of a distribution -- is central to the solution of many machine learning problems. However, when the distribution is discrete, most common…

Machine Learning · Statistics 2024-04-16 Jiaxin Shi , Yuhao Zhou , Jessica Hwang , Michalis K. Titsias , Lester Mackey

In our work, we propose a novel yet simple approach to obtain an adaptive learning rate for gradient-based descent methods on classification tasks. Instead of the traditional approach of selecting adaptive learning rates via the decayed…

Machine Learning · Computer Science 2023-04-21 Neel Mishra , Pawan Kumar

We present a new approach to automatic amortized inference in universal probabilistic programs which improves performance compared to current methods. Our approach is a variation of inference compilation (IC) which leverages deep neural…

Machine Learning · Computer Science 2019-10-29 William Harvey , Andreas Munk , Atılım Güneş Baydin , Alexander Bergholm , Frank Wood

A central challenge in program induction has long been the trade-off between symbolic and neural approaches. Symbolic methods offer compositional generalisation and data efficiency, yet their scalability is constrained by formalisms such as…

Machine Learning · Computer Science 2026-04-22 Matthew V. Macfarlane , Clément Bonnet , Herke van Hoof , Levi H. S. Lelis

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

We propose an optimization proxy in terms of iterative implicit gradient methods for solving constrained optimization problems with nonconvex loss functions. This framework can be applied to a broad range of machine learning settings,…

Optimization and Control · Mathematics 2025-10-14 Harshal D. Kaushik , Ming Jin

We study the problem of estimating from data, a sparse approximation to the inverse covariance matrix. Estimating a sparsity constrained inverse covariance matrix is a key component in Gaussian graphical model learning, but one that is…

Machine Learning · Statistics 2011-06-28 Suvrit Sra , Dongmin Kim

Learning in models with discrete latent variables is challenging due to high variance gradient estimators. Generally, approaches have relied on control variates to reduce the variance of the REINFORCE estimator. Recent work (Jang et al.…

Machine Learning · Computer Science 2017-11-07 George Tucker , Andriy Mnih , Chris J. Maddison , Dieterich Lawson , Jascha Sohl-Dickstein

We propose an adaptive (stochastic) gradient perturbation method for differentially private empirical risk minimization. At each iteration, the random noise added to the gradient is optimally adapted to the stepsize; we name this process…

Machine Learning · Computer Science 2021-10-26 Xiaoxia Wu , Lingxiao Wang , Irina Cristali , Quanquan Gu , Rebecca Willett

Among various supervised deep metric learning methods proxy-based approaches have achieved high retrieval accuracies. Proxies, which are class-representative points in an embedding space, receive updates based on proxy-sample similarities…

Computer Vision and Pattern Recognition · Computer Science 2022-11-21 Aoyu Li , Ikuro Sato , Kohta Ishikawa , Rei Kawakami , Rio Yokota