In this work we present an "out-of-the-box" application of Machine Learning (ML) optimizers for an industrial optimization problem. We introduce a piecewise polynomial model (spline) for fitting of $\mathcal{C}^k$-continuos functions, which can be deployed in a cam approximation setting. We then use the gradient descent optimization context provided by the machine learning framework TensorFlow to optimize the model parameters with respect to approximation quality and $\mathcal{C}^k$-continuity and evaluate available optimizers. Our experiments show that the problem solution is feasible using TensorFlow gradient tapes and that AMSGrad and SGD show the best results among available TensorFlow optimizers. Furthermore, we introduce a novel regularization approach to improve SGD convergence. Although experiments show that remaining discontinuities after optimization are small, we can eliminate these errors using a presented algorithm which has impact only on affected derivatives in the local spline segment.

Originally published on Towards AI the World's Leading AI and Technology News and Media Company. If you are building an AI-related product or service, we invite you to consider becoming an AI sponsor. At Towards AI, we help scale AI and technology startups. Let us help you unleash your technology to the masses. In this Mixed Model example, I will use a somewhat more advanced dataset containing the bodyweight growth of piglets across different levels.

The fully connected (FC) layer, one of the most fundamental modules in artificial neural networks (ANN), is often considered difficult and inefficient to train due to issues including the risk of overfitting caused by its large amount of parameters. Based on previous work studying ANN from linear spline perspectives, we propose a spline-based approach that eases the difficulty of training FC layers. Given some dataset, we first obtain a continuous piece-wise linear (CPWL) fit through spline methods such as multivariate adaptive regression spline (MARS). Next, we construct an ANN model from the linear spline model and continue to train the ANN model on the dataset using gradient descent optimization algorithms. Our experimental results and theoretical analysis show that our approach reduces the computational cost, accelerates the convergence of FC layers, and significantly increases the interpretability of the resulting model (FC layers) compared with standard ANN training with random parameter initialization followed by gradient descent optimizations.

Artificial intelligence (AI) systems have become increasingly common and the trend will continue. Examples of AI systems include autonomous vehicles (AV), computer vision, natural language processing, and AI medical experts. To allow for safe and effective deployment of AI systems, the reliability of such systems needs to be assessed. Traditionally, reliability assessment is based on reliability test data and the subsequent statistical modeling and analysis. The availability of reliability data for AI systems, however, is limited because such data are typically sensitive and proprietary. The California Department of Motor Vehicles (DMV) oversees and regulates an AV testing program, in which many AV manufacturers are conducting AV road tests. Manufacturers participating in the program are required to report recurrent disengagement events to California DMV. This information is being made available to the public. In this paper, we use recurrent disengagement events as a representation of the reliability of the AI system in AV, and propose a statistical framework for modeling and analyzing the recurrent events data from AV driving tests. We use traditional parametric models in software reliability and propose a new nonparametric model based on monotonic splines to describe the event process. We develop inference procedures for selecting the best models, quantifying uncertainty, and testing heterogeneity in the event process. We then analyze the recurrent events data from four AV manufacturers, and make inferences on the reliability of the AI systems in AV. We also describe how the proposed analysis can be applied to assess the reliability of other AI systems.

Smoothing splines provide a powerful and flexible means for nonparametric estimation and inference. With a cubic time complexity, fitting smoothing spline models to large data is computationally prohibitive. In this paper, we use the theoretical optimal eigenspace to derive a low rank approximation of the smoothing spline estimates. We develop a method to approximate the eigensystem when it is unknown and derive error bounds for the approximate estimates. The proposed methods are easy to implement with existing software. Extensive simulations show that the new methods are accurate, fast, and compares favorably against existing methods.

Atomistic or ab-initio molecular dynamics simulations are widely used to predict thermodynamics and kinetics and relate them to molecular structure. A common approach to go beyond the time- and lengthscales accessible with such computationally expensive simulations is the definition of coarse-grained molecular models. Existing coarse-graining approaches define an effective interaction potential to match defined properties of high-resolution models or experimental data. In this paper we reformulate coarse-graining as a supervised machine learning problem. We use statistical learning theory to decompose the coarse-graining error and cross-validation to select to compare the performance of different models. We introduce CGnets, a deep learning approach, that learn coarse-grained free energy functions and can be trained by the force matching scheme. CGnets maintain all physically relevant invariances and allow to incorporate prior physics knowledge to avoid sampling of unphysical structures. We demonstrate that CGnets outperform the results of classical coarse-graining methods, as they are able to capture the multi-body terms that emerge from the dimensionality reduction.

Hand-printed digits can be modeled as splines that are governed by about 8 control points.

Hand-printed digits can be modeled as splines that are governed by about 8 control points.