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Bayesian Neural Networks with Latent Variables (BNN+LVs) capture predictive uncertainty by explicitly modeling model uncertainty (via priors on network weights) and environmental stochasticity (via a latent input noise variable). In this work, we first show that BNN+LV suffers from a serious form of non-identifiability: explanatory power can be transferred between the model parameters and latent variables while fitting the data equally well. We demonstrate that as a result, in the limit of infinite data, the posterior mode over the network weights and latent variables is asymptotically biased away from the ground-truth. Due to this asymptotic bias, traditional inference methods may in practice yield parameters that generalize poorly and misestimate uncertainty. Next, we develop a novel inference procedure that explicitly mitigates the effects of likelihood non-identifiability during training and yields high-quality predictions as well as uncertainty estimates. We demonstrate that our inference method improves upon benchmark methods across a range of synthetic and real data-sets.

Variational Bayesian posterior inference often requires simplifying approximations such as mean-field parametrisation to ensure tractability. However, prior work has associated the variational mean-field approximation for Bayesian neural networks with underfitting in the case of small datasets or large model sizes. In this work, we show that invariances in the likelihood function of over-parametrised models contribute to this phenomenon because these invariances complicate the structure of the posterior by introducing discrete and/or continuous modes which cannot be well approximated by Gaussian mean-field distributions. In particular, we show that the mean-field approximation has an additional gap in the evidence lower bound compared to a purpose-built posterior that takes into account the known invariances. Importantly, this invariance gap is not constant; it vanishes as the approximation reverts to the prior. We proceed by first considering translation invariances in a linear model with a single data point in detail. We show that, while the true posterior can be constructed from a mean-field parametrisation, this is achieved only if the objective function takes into account the invariance gap. Then, we transfer our analysis of the linear model to neural networks. Our analysis provides a framework for future work to explore solutions to the invariance problem.

Optimal locomotion and efficient traversal of extraterrestrial rovers in dynamic terrains and environments is an important problem statement in the field of planetary science and geophysical systems. Designing a superlative and efficient architecture for the suspension mechanism of planetary rovers is a crucial step towards robust rovers. This paper focuses on the Rocker Bogie mechanism, a standard suspension methodology associated with foreign terrains. After scrutinizing the available previous literature and by leveraging various optimization and global minimization algorithms, this paper offers a novel study on mechanical design optimization of a rovers suspension mechanism. This paper presents extensive tests on Simulated Annealing, Genetic Algorithms, Swarm Intelligence techniques, Basin Hoping and Differential Evolution, while thoroughly assessing every related hyper parameter, to find utility driven solutions. We also assess Dual Annealing and subsidiary algorithms for the aforementioned task while maintaining an unbiased testing standpoint for ethical research. Computational efficiency and overall fitness are considered key valedictory parameters for assessing the related algorithms, emphasis is also given to variable input seeds to find the most suitable utility driven strategy. Simulated Annealing was obtained empirically to be the top performing heuristic strategy, with a fitness of 760, which was considerably superior to other algorithms and provided consistent performance across various input seeds and individual performance indicators.

A general framework with a series of different methods is proposed to improve the estimate of convex function (or functional) values when only noisy observations of the true input are available. Technically, our methods catch the bias introduced by the convexity and remove this bias from a baseline estimate. Theoretical analysis are conducted to show that the proposed methods can strictly reduce the expected estimate error under mild conditions. When applied, the methods require no specific knowledge about the problem except the convexity and the evaluation of the function. Therefore, they can serve as off-the-shelf tools to obtain good estimate for a wide range of problems, including optimization problems with random objective functions or constraints, and functionals of probability distributions such as the entropy and the Wasserstein distance. Numerical experiments on a wide variety of problems show that our methods can significantly improve the quality of the estimate compared with the baseline method.

The absolute value equations (AVE) problem is an algebraic problem of solving Ax+|x|=b. So far, most of the research focused on methods for solving AVEs, but we address the problem itself by analysing properties of AVE and the corresponding solution set. In particular, we investigate topological properties of the solution set, such as convexity, boundedness, connectedness, or whether it consists of finitely many solutions. Further, we address problems related to nonnegativity of solutions such as solvability or unique solvability. AVE can be formulated by means of different optimization problems, and in this regard we are interested in how the solutions of AVE are related with optima, Karush-Kuhn-Tucker points and feasible solutions of these optimization problems. We characterize the matrix classes associated with the above mentioned properties and inspect the computational complexity of the recognition problem; some of the classes are polynomially recognizable, but some others are proved to be NP-hard. For the intractable cases, we propose various sufficient conditions. We also post new challenging problems that raised during the investigation of the problem.

Tensegrity robots, composed of rigid rods and flexible cables, exhibit high strength-to-weight ratios and extreme deformations, enabling them to navigate unstructured terrain and even survive harsh impacts. However, they are hard to control due to their high dimensionality, complex dynamics, and coupled architecture. Physics-based simulation is one avenue for developing locomotion policies that can then be transferred to real robots, but modeling tensegrity robots is a complex task, so simulations experience a substantial sim2real gap. To address this issue, this paper describes a Real2Sim2Real strategy for tensegrity robots. This strategy is based on a differential physics engine that can be trained given limited data from a real robot (i.e. offline measurements and one random trajectory) and achieve a high enough accuracy to discover transferable locomotion policies. Beyond the overall pipeline, key contributions of this work include computing non-zero gradients at contact points, a loss function, and a trajectory segmentation technique that avoid conflicts in gradient evaluation during training. The proposed pipeline is demonstrated and evaluated on a real 3-bar tensegrity robot.

Human-in-the-loop aims to train an accurate prediction model with minimum cost by integrating human knowledge and experience. Humans can provide training data for machine learning applications and directly accomplish some tasks that are hard for computers in the pipeline with the help of machine-based approaches. In this paper, we survey existing works on human-in-the-loop from a data perspective and classify them into three categories with a progressive relationship: (1) the work of improving model performance from data processing, (2) the work of improving model performance through interventional model training, and (3) the design of the system independent human-in-the-loop. Using the above categorization, we summarize major approaches in the field, along with their technical strengths/ weaknesses, we have simple classification and discussion in natural language processing, computer vision, and others. Besides, we provide some open challenges and opportunities. This survey intends to provide a high-level summarization for human-in-the-loop and motivates interested readers to consider approaches for designing effective human-in-the-loop solutions.

This book develops an effective theory approach to understanding deep neural networks of practical relevance. Beginning from a first-principles component-level picture of networks, we explain how to determine an accurate description of the output of trained networks by solving layer-to-layer iteration equations and nonlinear learning dynamics. A main result is that the predictions of networks are described by nearly-Gaussian distributions, with the depth-to-width aspect ratio of the network controlling the deviations from the infinite-width Gaussian description. We explain how these effectively-deep networks learn nontrivial representations from training and more broadly analyze the mechanism of representation learning for nonlinear models. From a nearly-kernel-methods perspective, we find that the dependence of such models' predictions on the underlying learning algorithm can be expressed in a simple and universal way. To obtain these results, we develop the notion of representation group flow (RG flow) to characterize the propagation of signals through the network. By tuning networks to criticality, we give a practical solution to the exploding and vanishing gradient problem. We further explain how RG flow leads to near-universal behavior and lets us categorize networks built from different activation functions into universality classes. Altogether, we show that the depth-to-width ratio governs the effective model complexity of the ensemble of trained networks. By using information-theoretic techniques, we estimate the optimal aspect ratio at which we expect the network to be practically most useful and show how residual connections can be used to push this scale to arbitrary depths. With these tools, we can learn in detail about the inductive bias of architectures, hyperparameters, and optimizers.

This paper focuses on the expected difference in borrower's repayment when there is a change in the lender's credit decisions. Classical estimators overlook the confounding effects and hence the estimation error can be magnificent. As such, we propose another approach to construct the estimators such that the error can be greatly reduced. The proposed estimators are shown to be unbiased, consistent, and robust through a combination of theoretical analysis and numerical testing. Moreover, we compare the power of estimating the causal quantities between the classical estimators and the proposed estimators. The comparison is tested across a wide range of models, including linear regression models, tree-based models, and neural network-based models, under different simulated datasets that exhibit different levels of causality, different degrees of nonlinearity, and different distributional properties. Most importantly, we apply our approaches to a large observational dataset provided by a global technology firm that operates in both the e-commerce and the lending business. We find that the relative reduction of estimation error is strikingly substantial if the causal effects are accounted for correctly.

Substantial progress has been made recently on developing provably accurate and efficient algorithms for low-rank matrix factorization via nonconvex optimization. While conventional wisdom often takes a dim view of nonconvex optimization algorithms due to their susceptibility to spurious local minima, simple iterative methods such as gradient descent have been remarkably successful in practice. The theoretical footings, however, had been largely lacking until recently. In this tutorial-style overview, we highlight the important role of statistical models in enabling efficient nonconvex optimization with performance guarantees. We review two contrasting approaches: (1) two-stage algorithms, which consist of a tailored initialization step followed by successive refinement; and (2) global landscape analysis and initialization-free algorithms. Several canonical matrix factorization problems are discussed, including but not limited to matrix sensing, phase retrieval, matrix completion, blind deconvolution, robust principal component analysis, phase synchronization, and joint alignment. Special care is taken to illustrate the key technical insights underlying their analyses. This article serves as a testament that the integrated consideration of optimization and statistics leads to fruitful research findings.