Differentiable simulation is a promising toolkit for fast gradient-based policy optimization and system identification. However, existing approaches to differentiable simulation have largely tackled scenarios where obtaining smooth gradients has been relatively easy, such as systems with mostly smooth dynamics. In this work, we study the challenges that differentiable simulation presents when it is not feasible to expect that a single descent reaches a global optimum, which is often a problem in contact-rich scenarios. We analyze the optimization landscapes of diverse scenarios that contain both rigid bodies and deformable objects. In dynamic environments with highly deformable objects and fluids, differentiable simulators produce rugged landscapes with nonetheless useful gradients in some parts of the space. We propose a method that combines Bayesian optimization with semi-local 'leaps' to obtain a global search method that can use gradients effectively, while also maintaining robust performance in regions with noisy gradients. We show that our approach outperforms several gradient-based and gradient-free baselines on an extensive set of experiments in simulation, and also validate the method using experiments with a real robot and deformables. Videos and supplementary materials are available at https://tinyurl.com/globdiff

The implicit stochastic gradient descent (ISGD), a proximal version of SGD, is gaining interest in the literature due to its stability over (explicit) SGD. In this paper, we conduct an in-depth analysis of the two modes of ISGD for smooth convex functions, namely proximal Robbins-Monro (proxRM) and proximal Poylak-Ruppert (proxPR) procedures, for their use in statistical inference on model parameters. Specifically, we derive non-asymptotic point estimation error bounds of both proxRM and proxPR iterates and their limiting distributions, and propose on-line estimators of their asymptotic covariance matrices that require only a single run of ISGD. The latter estimators are used to construct valid confidence intervals for the model parameters. Our analysis is free of the generalized linear model assumption that has limited the preceding analyses, and employs feasible procedures. Our on-line covariance matrix estimators appear to be the first of this kind in the ISGD literature.

Kernel ridge regression (KRR) has recently attracted renewed interest due to its potential for explaining the transient effects, such as double descent, that emerge during neural network training. In this work, we study how the alignment between the target function and the kernel affects the performance of the KRR. We focus on the truncated KRR (TKRR) which utilizes an additional parameter that controls the spectral truncation of the kernel matrix. We show that for polynomial alignment, there is an \emph{over-aligned} regime, in which TKRR can achieve a faster rate than what is achievable by full KRR. The rate of TKRR can improve all the way to the parametric rate, while that of full KRR is capped at a sub-optimal value. This shows that target alignemnt can be better leveraged by utilizing spectral truncation in kernel methods. We also consider the bandlimited alignment setting and show that the regularization surface of TKRR can exhibit transient effects including multiple descent and non-monotonic behavior. Our results show that there is a strong and quantifable relation between the shape of the \emph{alignment spectrum} and the generalization performance of kernel methods, both in terms of rates and in finite samples.

The electron density of a molecule or material has recently received major attention as a target quantity of machine-learning models. A natural choice to construct a model that yields transferable and linear-scaling predictions is to represent the scalar field using a multi-centered atomic basis analogous to that routinely used in density fitting approximations. However, the non-orthogonality of the basis poses challenges for the learning exercise, as it requires accounting for all the atomic density components at once. We devise a gradient-based approach to directly minimize the loss function of the regression problem in an optimized and highly sparse feature space. In so doing, we overcome the limitations associated with adopting an atom-centered model to learn the electron density over arbitrarily complex datasets, obtaining extremely accurate predictions. The enhanced framework is tested on 32-molecule periodic cells of liquid water, presenting enough complexity to require an optimal balance between accuracy and computational efficiency. We show that starting from the predicted density a single Kohn-Sham diagonalization step can be performed to access total energy components that carry an error of just 0.1 meV/atom with respect to the reference density functional calculations. Finally, we test our method on the highly heterogeneous QM9 benchmark dataset, showing that a small fraction of the training data is enough to derive ground-state total energies within chemical accuracy.

Inferring causal relationships from observational data is rarely straightforward, but the problem is especially difficult in high dimensions. For these applications, causal discovery algorithms typically require parametric restrictions or extreme sparsity constraints. We relax these assumptions and focus on an important but more specialized problem, namely recovering the causal order among a subgraph of variables known to descend from some (possibly large) set of confounding covariates, i.e. a $\textit{confounder blanket}$. This is useful in many settings, for example when studying a dynamic biomolecular subsystem with genetic data providing background information. Under a structural assumption called the $\textit{confounder blanket principle}$, which we argue is essential for tractable causal discovery in high dimensions, our method accommodates graphs of low or high sparsity while maintaining polynomial time complexity. We present a structure learning algorithm that is provably sound and complete with respect to a so-called $\textit{lazy oracle}$. We design inference procedures with finite sample error control for linear and nonlinear systems, and demonstrate our approach on a range of simulated and real-world datasets. An accompanying $\texttt{R}$ package, $\texttt{cbl}$, is available from $\texttt{CRAN}$.

Software packages like TensorFlow and PyTorch are designed to support linear algebra operations, and their speed and usability determine their success. However, by prioritising speed, they often neglect memory requirements. As a consequence, the implementations of memory-intensive algorithms that are convenient in terms of software design can often not be run for large problems due to memory overflows. Memory-efficient solutions require complex programming approaches with significant logic outside the computational framework. This impairs the adoption and use of such algorithms. To address this, we developed an XLA compiler extension that adjusts the computational data-flow representation of an algorithm according to a user-specified memory limit. We show that k-nearest neighbour and sparse Gaussian process regression methods can be run at a much larger scale on a single device, where standard implementations would have failed. Our approach leads to better use of hardware resources. We believe that further focus on removing memory constraints at a compiler level will widen the range of machine learning methods that can be developed in the future.

Sarcasm is a term that refers to the use of words to mock, irritate, or amuse someone. It is commonly used on social media. The metaphorical and creative nature of sarcasm presents a significant difficulty for sentiment analysis systems based on affective computing. The methodology and results of our team, UTNLP, in the SemEval-2022 shared task 6 on sarcasm detection are presented in this paper. We put different models, and data augmentation approaches to the test and report on which one works best. The tests begin with traditional machine learning models and progress to transformer-based and attention-based models. We employed data augmentation based on data mutation and data generation. Using RoBERTa and mutation-based data augmentation, our best approach achieved an F1-sarcastic of 0.38 in the competition's evaluation phase. After the competition, we fixed our model's flaws and achieved an F1-sarcastic of 0.414.

K Nearest Neighbors or KNN is a standard Machine Learning algorithm used for classification. In KNN, we plot already labeled points with their label and then define decision boundaries based on the value of the hyperparameter "K". Hyperparameter just means a parameter that we control and can use for tuning. "K" is used to represent how many of the nearest neighbors we should take into account when determining the class of a new point. In this post we'll cover how to do KNN on two datasets, one contrived sample dataset and one more realistic dataset about wine from sklearn.

In most data-scientific approaches, the principle of Maximum Entropy (MaxEnt) is used to a posteriori justify some parametric model which has been already chosen based on experience, prior knowledge or computational simplicity. In a perpendicular formulation to conventional model building, we start from the linear system of phenomenological constraints and asymptotically derive the distribution over all viable distributions that satisfy the provided set of constraints. The MaxEnt distribution plays a special role, as it is the most typical among all phenomenologically viable distributions representing a good expansion point for large-N techniques. This enables us to consistently formulate hypothesis testing in a fully-data driven manner. The appropriate parametric model which is supported by the data can be always deduced at the end of model selection. In the MaxEnt framework, we recover major scores and selection procedures used in multiple applications and assess their ability to capture associations in the data-generating process and identify the most generalizable model. This data-driven counterpart of standard model selection demonstrates the unifying prospective of the deductive logic advocated by MaxEnt principle, while potentially shedding new insights to the inverse problem.

The generalization of machine learning models has a complex dependence on the data, model and learning algorithm. We study train and test performance, as well as the generalization gap given by the mean of their difference over different data set samples to understand their ``typical" behavior. We derive an expression for the gap as a function of the covariance between the model parameter distribution and the train loss, and another expression for the average test performance, showing test generalization only depends on data-averaged parameter distribution and the data-averaged loss. We show that for a large class of model parameter distributions a modified generalization gap is always non-negative. By specializing further to parameter distributions produced by stochastic gradient descent (SGD), along with a few approximations and modeling considerations, we are able to predict some aspects about how the generalization gap and model train and test performance vary as a function of SGD noise. We evaluate these predictions empirically on the Cifar10 classification task based on a ResNet architecture.