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Reasoning about a model's accuracy on a test sample from its confidence is a central problem in machine learning, being connected to important applications such as uncertainty representation, model selection, and exploration. While these connections have been well-studied in the i.i.d. settings, distribution shifts pose significant challenges to the traditional methods. Therefore, model calibration and model selection remain challenging in the unsupervised domain adaptation problem--a scenario where the goal is to perform well in a distribution shifted domain without labels. In this work, we tackle difficulties coming from distribution shifts by developing a novel importance weighted group accuracy estimator. Specifically, we formulate an optimization problem for finding an importance weight that leads to an accurate group accuracy estimation in the distribution shifted domain with theoretical analyses. Extensive experiments show the effectiveness of group accuracy estimation on model calibration and model selection. Our results emphasize the significance of group accuracy estimation for addressing challenges in unsupervised domain adaptation, as an orthogonal improvement direction with improving transferability of accuracy.

Engineers are often faced with the decision to select the most appropriate model for simulating the behavior of engineered systems, among a candidate set of models. Experimental monitoring data can generate significant value by supporting engineers toward such decisions. Such data can be leveraged within a Bayesian model updating process, enabling the uncertainty-aware calibration of any candidate model. The model selection task can subsequently be cast into a problem of decision-making under uncertainty, where one seeks to select the model that yields an optimal balance between the reward associated with model precision, in terms of recovering target Quantities of Interest (QoI), and the cost of each model, in terms of complexity and compute time. In this work, we examine the model selection task by means of Bayesian decision theory, under the prism of availability of models of various refinements, and thus varying levels of fidelity. In doing so, we offer an exemplary application of this framework on the IMAC-MVUQ Round-Robin Challenge. Numerical investigations show various outcomes of model selection depending on the target QoI.

Achieving accurate approximations to solutions of large linear systems is crucial, especially when those systems utilize real-world data. A consequence of using real-world data is that there will inevitably be missingness. Current approaches for dealing with missing data, such as deletion and imputation, can introduce bias. Recent studies proposed an adaptation of stochastic gradient descent (SGD) in specific missing-data models. In this work, we propose a new algorithm, $\ell$-tuple mSGD, for the setting in which data is missing in a block-wise, tuple pattern. We prove that our proposed method uses unbiased estimates of the gradient of the least squares objective in the presence of tuple missing data. We also draw connections between $\ell$-tuple mSGD and previously established SGD-type methods for missing data. Furthermore, we prove our algorithm converges when using updating step sizes and empirically demonstrate the convergence of $\ell$-tuple mSGD on synthetic data. Lastly, we evaluate $\ell$-tuple mSGD applied to real-world continuous glucose monitoring (CGM) device data.

As models grow larger and more complex, achieving better off-sample generalization with minimal trial-and-error is critical to the reliability and economy of machine learning workflows. As a proxy for the well-studied heuristic of seeking "flat" local minima, gradient regularization is a natural avenue, and first-order approximations such as Flooding and sharpness-aware minimization (SAM) have received significant attention, but their performance depends critically on hyperparameters (flood threshold and neighborhood radius, respectively) that are non-trivial to specify in advance. In order to develop a procedure which is more resilient to misspecified hyperparameters, with the hard-threshold "ascent-descent" switching device used in Flooding as motivation, we propose a softened, pointwise mechanism called SoftAD that downweights points on the borderline, limits the effects of outliers, and retains the ascent-descent effect. We contrast formal stationarity guarantees with those for Flooding, and empirically demonstrate how SoftAD can realize classification accuracy competitive with SAM and Flooding while maintaining a much smaller loss generalization gap and model norm. Our empirical tests range from simple binary classification on the plane to image classification using neural networks with millions of parameters; the key trends are observed across all datasets and models studied, and suggest a potential new approach to implicit regularization.

This paper presents a method using data-driven models for selecting actions and predicting the total performance of autonomous wheel loader operations over many loading cycles in a changing environment. The performance includes loaded mass, loading time, work. The data-driven models input the control parameters of a loading action and the heightmap of the initial pile state to output the inference of either the performance or the resulting pile state. By iteratively utilizing the resulting pile state as the initial pile state for consecutive predictions, the prediction method enables long-horizon forecasting. Deep neural networks were trained on data from over 10,000 random loading actions in gravel piles of different shapes using 3D multibody dynamics simulation. The models predict the performance and the resulting pile state with, on average, 95% accuracy in 1.2 ms, and 97% in 4.5 ms, respectively. The performance prediction was found to be even faster in exchange for accuracy by reducing the model size with the lower dimensional representation of the pile state using its slope and curvature. The feasibility of long-horizon predictions was confirmed with 40 sequential loading actions at a large pile. With the aid of a physics-based model, the pile state predictions are kept sufficiently accurate for longer-horizon use.

The initial interaction of a user with a recommender system is problematic because, in such a so-called cold start situation, the recommender system has very little information about the user, if any. Moreover, in collaborative filtering, users need to share their preferences with the service provider by rating items while in content-based filtering there is no need for such information sharing. We have recently shown that a content-based model that uses hypercube graphs can determine user preferences with a very limited number of ratings while better preserving user privacy. In this paper, we confirm these findings on the basis of experiments with more than 1,000 users in the restaurant and movie domains. We show that the proposed method outperforms standard machine learning algorithms when the number of available ratings is at most 10, which often happens, and is competitive with larger training sets. In addition, training is simple and does not require large computational efforts.

Gaussian boson sampling, a computational model that is widely believed to admit quantum supremacy, has already been experimentally demonstrated and is claimed to surpass the classical simulation capabilities of even the most powerful supercomputers today. However, whether the current approach limited by photon loss and noise in such experiments prescribes a scalable path to quantum advantage is an open question. To understand the effect of photon loss on the scalability of Gaussian boson sampling, we analytically derive the asymptotic operator entanglement entropy scaling, which relates to the simulation complexity. As a result, we observe that efficient tensor network simulations are likely possible under the $N_\text{out}\propto\sqrt{N}$ scaling of the number of surviving photons orange$N_\text{out}$ in the number of input photons $N$. We numerically verify this result using a tensor network algorithm with $U(1)$ symmetry, and overcome previous challenges due to the large local Hilbert space dimensions in Gaussian boson sampling with hardware acceleration. Additionally, we observe that increasing the photon number through larger squeezing does not increase the entanglement entropy significantly. Finally, we numerically find the bond dimension necessary for fixed accuracy simulations, providing more direct evidence for the complexity of tensor networks.

A key challenge when trying to understand innovation is that it is a dynamic, ongoing process, which can be highly contingent on ephemeral factors such as culture, economics, or luck. This means that any analysis of the real-world process must necessarily be historical - and thus probably too late to be most useful - but also cannot be sure what the properties of the web of connections between innovations is or was. Here I try to address this by designing and generating a set of synthetic innovation web "dictionaries" that can be used to host sampled innovation timelines, probe the overall statistics and behaviours of these processes, and determine the degree of their reliance on the structure or generating algorithm. Thus, inspired by the work of Fink, Reeves, Palma and Farr (2017) on innovation in language, gastronomy, and technology, I study how new symbol discovery manifests itself in terms of additional "word" vocabulary being available from dictionaries generated from a finite number of symbols. Several distinct dictionary generation models are investigated using numerical simulation, with emphasis on the scaling of knowledge as dictionary generators and parameters are varied, and the role of which order the symbols are discovered in.

Learning curves are a measure for how the performance of machine learning models improves given a certain volume of training data. Over a wide variety of applications and models it was observed that learning curves follow -- to a large extent -- a power law behavior. This makes the performance of different models for a given task somewhat predictable and opens the opportunity to reduce the training time for practitioners, who are exploring the space of possible models and hyperparameters for the problem at hand. By estimating the learning curve of a model from training on small subsets of data only the best models need to be considered for training on the full dataset. How to choose subset sizes and how often to sample models on these to obtain estimates is however not researched. Given that the goal is to reduce overall training time strategies are needed that sample the performance in a time-efficient way and yet leads to accurate learning curve estimates. In this paper we formulate the framework for these strategies and propose several strategies. Further we evaluate the strategies for simulated learning curves and in experiments with popular datasets and models for image classification tasks.

In human-AI collaboration systems for critical applications, in order to ensure minimal error, users should set an operating point based on model confidence to determine when the decision should be delegated to human experts. Samples for which model confidence is lower than the operating point would be manually analysed by experts to avoid mistakes. Such systems can become truly useful only if they consider two aspects: models should be confident only for samples for which they are accurate, and the number of samples delegated to experts should be minimized. The latter aspect is especially crucial for applications where available expert time is limited and expensive, such as healthcare. The trade-off between the model accuracy and the number of samples delegated to experts can be represented by a curve that is similar to an ROC curve, which we refer to as confidence operating characteristic (COC) curve. In this paper, we argue that deep neural networks should be trained by taking into account both accuracy and expert load and, to that end, propose a new complementary loss function for classification that maximizes the area under this COC curve. This promotes simultaneously the increase in network accuracy and the reduction in number of samples delegated to humans. We perform experiments on multiple computer vision and medical image datasets for classification. Our results demonstrate that the proposed loss improves classification accuracy and delegates less number of decisions to experts, achieves better out-of-distribution samples detection and on par calibration performance compared to existing loss functions.