Mathematical proof aims to deliver confident conclusions, but a very similar process of deduction can be used to make uncertain estimates that are open to revision. A key ingredient in such reasoning is the use of a "default" estimate of $\mathbb{E}[XY] = \mathbb{E}[X] \mathbb{E}[Y]$ in the absence of any specific information about the correlation between $X$ and $Y$, which we call *the presumption of independence*. Reasoning based on this heuristic is commonplace, intuitively compelling, and often quite successful -- but completely informal. In this paper we introduce the concept of a heuristic estimator as a potential formalization of this type of defeasible reasoning. We introduce a set of intuitively desirable coherence properties for heuristic estimators that are not satisfied by any existing candidates. Then we present our main open problem: is there a heuristic estimator that formalizes intuitively valid applications of the presumption of independence without also accepting spurious arguments?

Natural Language Processing helps machines understand and analyze natural languages. NLP is an automated process that helps extract the required information from data by applying machine learning algorithms. Learning NLP will help you land a high-paying job as it is used by various professionals such as data scientist professionals, machine learning engineers, etc. We have compiled a comprehensive list of NLP Interview Questions and Answers that will help you prepare for your upcoming interviews. You can also check out these free NLP courses to help with your preparation. Once you have prepared the following commonly asked questions, you can get into the job role you are looking for. Without further ado, let's kickstart your NLP learning journey.

Bayesian optimization has emerged at the forefront of expensive black-box optimization due to its data efficiency. Recent years have witnessed a proliferation of studies on the development of new Bayesian optimization algorithms and their applications. Hence, this paper attempts to provide a comprehensive and updated survey of recent advances in Bayesian optimization and identify interesting open problems. We categorize the existing work on Bayesian optimization into nine main groups according to the motivations and focus of the proposed algorithms. For each category, we present the main advances with respect to the construction of surrogate models and adaptation of the acquisition functions. Finally, we discuss the open questions and suggest promising future research directions, in particular with regard to heterogeneity, privacy preservation, and fairness in distributed and federated optimization systems.

Bayesian inference has theoretical attractions as a principled framework for reasoning about beliefs. However, the motivations of Bayesian inference which claim it to be the only 'rational' kind of reasoning do not apply in practice. They create a binary split in which all approximate inference is equally 'irrational'. Instead, we should ask ourselves how to define a spectrum of more- and less-rational reasoning that explains why we might prefer one Bayesian approximation to another. I explore approximate inference in Bayesian neural networks and consider the unintended interactions between the probabilistic model, approximating distribution, optimization algorithm, and dataset. The complexity of these interactions highlights the difficulty of any strategy for evaluating Bayesian approximations which focuses entirely on the method, outside the context of specific datasets and decision-problems. For given applications, the expected utility of the approximate posterior can measure inference quality. To assess a model's ability to incorporate different parts of the Bayesian framework we can identify desirable characteristic behaviours of Bayesian reasoning and pick decision-problems that make heavy use of those behaviours. Here, we use continual learning (testing the ability to update sequentially) and active learning (testing the ability to represent credence). But existing continual and active learning set-ups pose challenges that have nothing to do with posterior quality which can distort their ability to evaluate Bayesian approximations. These unrelated challenges can be removed or reduced, allowing better evaluation of approximate inference methods.

Sparse modelling or model selection with categorical data is challenging even for a moderate number of variables, because one parameter is roughly needed to encode one category or level. The Group Lasso is a well known efficient algorithm for selection continuous or categorical variables, but all estimates related to a selected factor usually differ. Therefore, a fitted model may not be sparse, which makes the model interpretation difficult. To obtain a sparse solution of the Group Lasso we propose the following two-step procedure: first, we reduce data dimensionality using the Group Lasso; then to choose the final model we use an information criterion on a small family of models prepared by clustering levels of individual factors. We investigate selection correctness of the algorithm in a sparse high-dimensional scenario. We also test our method on synthetic as well as real datasets and show that it performs better than the state of the art algorithms with respect to the prediction accuracy or model dimension.

Learning causal structure is useful in many areas of artificial intelligence, including planning, robotics, and explanation. Constraint-based structure learning algorithms such as PC use conditional independence (CI) tests to infer causal structure. Traditionally, constraint-based algorithms perform CI tests with a preference for smaller-sized conditioning sets, partially because the statistical power of conventional CI tests declines rapidly as the size of the conditioning set increases. However, many modern conditional independence tests are model-based, and these tests use well-regularized models that maintain statistical power even with very large conditioning sets. This suggests an intriguing new strategy for constraint-based algorithms which may result in a reduction of the total number of CI tests performed: Test variable pairs with large conditioning sets first, as a pre-processing step that finds some conditional independencies quickly, before moving on to the more conventional strategy that favors small conditioning sets. We propose such a pre-processing step for the PC algorithm which relies on performing CI tests on a few randomly selected large conditioning sets. We perform an empirical analysis on directed acyclic graphs (DAGs) that correspond to real-world systems and both empirical and theoretical analyses for Erd\H{o}s-Renyi DAGs. Our results show that Pre-Processing Plus PC (P3PC) performs far fewer CI tests than the original PC algorithm, between 0.5% to 36%, and often less than 10%, of the CI tests that the PC algorithm alone performs. The efficiency gains are particularly significant for the DAGs corresponding to real-world systems.

Epistemic uncertainty quantification is a crucial part of drawing credible conclusions from predictive models, whether concerned about the prediction at a given point or any downstream evaluation that uses the model as input. When the predictive model is simple and its evaluation differentiable, this task is solved by the delta method, where we propagate the asymptotically-normal uncertainty in the predictive model through the evaluation to compute standard errors and Wald confidence intervals. However, this becomes difficult when the model and/or evaluation becomes more complex. Remedies include the bootstrap, but it can be computationally infeasible when training the model even once is costly. In this paper, we propose an alternative, the implicit delta method, which works by infinitesimally regularizing the training loss of the predictive model to automatically assess downstream uncertainty. We show that the change in the evaluation due to regularization is consistent for the asymptotic variance of the evaluation estimator, even when the infinitesimal change is approximated by a finite difference. This provides both a reliable quantification of uncertainty in terms of standard errors as well as permits the construction of calibrated confidence intervals. We discuss connections to other approaches to uncertainty quantification, both Bayesian and frequentist, and demonstrate our approach empirically.

Uncertainty quantification (UQ) has increasing importance in building robust high-performance and generalizable materials property prediction models. It can also be used in active learning to train better models by focusing on getting new training data from uncertain regions. There are several categories of UQ methods each considering different types of uncertainty sources. Here we conduct a comprehensive evaluation on the UQ methods for graph neural network based materials property prediction and evaluate how they truly reflect the uncertainty that we want in error bound estimation or active learning. Our experimental results over four crystal materials datasets (including formation energy, adsorption energy, total energy, and band gap properties) show that the popular ensemble methods for uncertainty estimation is NOT the best choice for UQ in materials property prediction. For the convenience of the community, all the source code and data sets can be accessed freely at \url{https://github.com/usccolumbia/materialsUQ}.

Here we aimed to use biologically relevant neuron models connected in a brain-like network structure to study its potential to achieve input separation in a robotic system interacting with real-world objects. The model network was inspired by local cortical networks in its recursive structure in principle, though with much fewer neurons and without the ambition to precisely mimick any assumed specific network structure. The aim was to explore if the inherent dynamic properties in such networks in themselves were enough to achieve efficient object classification. Our model system is reminiscent of Reservoir Computing networks (i.e. Gauthier et al 2020 Nature Communications), but our neurons have state memory, i.e. dynamics, which are biologically relevant. Moreover, the population of neurons are split into excitatory and inhibitory neurons. Combined with the neuronal output thresholding, i.e. imparting nonlinearity to the networks when inhibition drives the neurons below their thresholds, and combined with biologically relevant conduction delays, this setting creates extraordinarily rich network dynamics. Motivation for: what would be required in the robotics design to explore the questions we set out to explore? How well could we live up to those requirements with the robotics system used?

Backpropagation applied to handwritten zip code recognition.