Neural control variates (NCVs) have emerged as a powerful tool for variance reduction in Monte Carlo (MC) simulations, particularly in high-dimensional problems where traditional control variates are difficult to construct analytically. By training neural networks to learn auxiliary functions correlated with the target observable, NCVs can significantly reduce estimator variance while preserving unbiasedness. However, a critical but often overlooked aspect of NCV training is the role of autocorrelated samples generated by Markov Chain Monte Carlo (MCMC). While such samples are typically discarded for error estimation due to their statistical redundancy, they may contain useful information about the structure of the underlying probability distribution that can benefit the training process. In this work, we systematically examine the effect of using correlated configurations in training neural control variates. We demonstrate, both conceptually and numerically, that training on correlated data can improve control variate performance, especially in settings with limited computational resources. Our analysis includes empirical results from $U(1)$ gauge theory and scalar field theory, illustrating when and how autocorrelated samples enhance NCV construction. These findings provide practical guidance for the efficient use of MCMC data in training neural networks.

We formulate the problem of constructing multiple simultaneously valid confidence intervals (CIs) as estimating a high probability upper bound on the maximum error for a class/set of estimate-estimand-error tuples, and refer to this as the error estimation problem. For a single such tuple, data-driven confidence intervals can often be used to bound the error in our estimate. However, for a class of estimate-estimand-error tuples, nontrivial high probability upper bounds on the maximum error often require class complexity as input -- limiting the practicality of such methods and often resulting in loose bounds. Rather than deriving theoretical class complexity-based bounds, we propose a completely data-driven approach to estimate an upper bound on the maximum error. The simple and general nature of our solution to this fundamental challenge lends itself to several applications including: multiple CI construction, multiple hypothesis testing, estimating excess risk bounds (a fundamental measure of uncertainty in machine learning) for any training/fine-tuning algorithm, and enabling the development of a contextual bandit pipeline that can leverage any reward model estimation procedure as input (without additional mathematical analysis).

In traditional Machine Learning, the algorithms predictions are based on the assumption that the data follows the same distribution in both the training and the test datasets. However, in real world data this condition does not hold and, for instance, the distribution of the covariates changes whereas the conditional distribution of the targets remains unchanged. This situation is called covariate shift problem where standard error estimation may be no longer accurate. In this context, the importance is a measure commonly used to alleviate the influence of covariate shift on error estimations. The main drawback is that it is not easy to compute. The Kullback-Leibler Importance Estimation Procedure (KLIEP) is capable of estimating importance in a promising way. Despite its good performance, it fails to ignore target information, since it only includes the covariates information for computing the importance. In this direction, this paper explores the potential performance improvement if target information is considered in the computation of the importance. Then, a redefinition of the importance arises in order to be generalized in this way. Besides the potential improvement in performance, including target information make possible the application to a real application about plankton classification that motivates this research and characterized by its great dimensionality, since considering targets rather than covariates reduces the computation and the noise in the covariates. The impact of taking target information is also explored when Logistic Regression (LR), Kernel Mean Matching (KMM), Ensemble Kernel Mean Matching (EKMM) and the naive predecessor of KLIEP called Kernel Density Estimation (KDE) methods estimate the importance. The experimental results lead to a more accurate error estimation using target information, especially in case of the more promising method KLIEP.

In machine learning models, the estimation of errors is often complex due to distribution bias, particularly in spatial data such as those found in environmental studies. We introduce an approach based on the ideas of importance sampling to obtain an unbiased estimate of the target error. By taking into account difference between desirable error and available data, our method reweights errors at each sample point and neutralizes the shift. Importance sampling technique and kernel density estimation were used for reweighteing. We validate the effectiveness of our approach using artificial data that resemble real-world spatial datasets. Our findings demonstrate advantages of the proposed approach for the estimation of the target error, offering a solution to a distribution shift problem. Overall error of predictions dropped from 7% to just 2% and it gets smaller for larger samples.

Efficient and accurate segmentation of unseen objects is crucial for robotic manipulation. However, it remains challenging due to over- or under-segmentation. Although existing refinement methods can enhance the segmentation quality, they fix only minor boundary errors or are not sufficiently fast. In this work, we propose INSTAnce Boundary Explicit Error Estimation and Refinement (INSTA-BEEER), a novel refinement model that allows for adding and deleting instances and sharpening boundaries. Leveraging an error-estimation-then-refinement scheme, the model first estimates the pixel-wise boundary explicit errors: true positive, true negative, false positive, and false negative pixels of the instance boundary in the initial segmentation. It then refines the initial segmentation using these error estimates as guidance. Experiments show that the proposed model significantly enhances segmentation, achieving state-of-the-art performance. Furthermore, with a fast runtime (less than 0.1 s), the model consistently improves performance across various initial segmentation methods, making it highly suitable for practical robotic applications.

Neural network-based decisions tend to be overconfident, where their raw outcome probabilities do not align with the true decision probabilities. Calibration of neural networks is an essential step towards more reliable deep learning frameworks. Prior metrics of calibration error primarily utilize crisp bin membership-based measures. This exacerbates skew in model probabilities and portrays an incomplete picture of calibration error. In this work, we propose a Fuzzy Calibration Error metric (FCE) that utilizes a fuzzy binning approach to calculate calibration error. This approach alleviates the impact of probability skew and provides a tighter estimate while measuring calibration error. We compare our metric with ECE across different data populations and class memberships. Our results show that FCE offers better calibration error estimation, especially in multi-class settings, alleviating the effects of skew in model confidence scores on calibration error estimation. We make our code and supplementary materials available at: https://github.com/bihani-g/fce

Random Fourier Features (RFF) is among the most popular and broadly applicable approaches for scaling up kernel methods. In essence, RFF allows the user to avoid costly computations on a large kernel matrix via a fast randomized approximation. However, a pervasive difficulty in applying RFF is that the user does not know the actual error of the approximation, or how this error will propagate into downstream learning tasks. Up to now, the RFF literature has primarily dealt with these uncertainties using theoretical error bounds, but from a user's standpoint, such results are typically impractical -- either because they are highly conservative or involve unknown quantities. To tackle these general issues in a data-driven way, this paper develops a bootstrap approach to numerically estimate the errors of RFF approximations. Three key advantages of this approach are: (1) The error estimates are specific to the problem at hand, avoiding the pessimism of worst-case bounds. (2) The approach is flexible with respect to different uses of RFF, and can even estimate errors in downstream learning tasks. (3) The approach enables adaptive computation, so that the user can quickly inspect the error of a rough initial kernel approximation and then predict how much extra work is needed. Lastly, in exchange for all of these benefits, the error estimates can be obtained at a modest computational cost.

Complex prediction models such as deep learning are the output from fitting machine learning, neural networks, or AI models to a set of training data. These are now standard tools in science. A key challenge with the current generation of models is that they are highly parameterized, which makes describing and interpreting the prediction strategies difficult. We use topological data analysis to transform these complex prediction models into pictures representing a topological view. The result is a map of the predictions that enables inspection. The methods scale up to large datasets across different domains and enable us to detect labeling errors in training data, understand generalization in image classification, and inspect predictions of likely pathogenic mutations in the BRCA1 gene.

Even though a train/test split of the dataset randomly performed is a common practice, could not always be the best approach for estimating performance generalization under some scenarios. The fact is that the usual machine learning methodology can sometimes overestimate the generalization error when a dataset is not representative or when rare and elusive examples are a fundamental aspect of the detection problem. In the present work, we analyze strategies based on the predictors' variability to split in training and testing sets. Such strategies aim at guaranteeing the inclusion of rare or unusual examples with a minimal loss of the population's representativeness and provide a more accurate estimation about the generalization error when the dataset is not representative. Two baseline classifiers based on decision trees were used for testing the four splitting strategies considered. Both classifiers were applied on CTU19 a low-representative dataset for a network security detection problem. Preliminary results showed the importance of applying the three alternative strategies to the Monte Carlo splitting strategy in order to get a more accurate error estimation on different but feasible scenarios.

Physics-informed neural networks (PINNs) are one popular approach to incorporate a priori knowledge about physical systems into the learning framework. PINNs are known to be robust for smaller training sets, derive better generalization problems, and are faster to train. In this paper, we show that using PINNs in comparison with purely data-driven neural networks is not only favorable for training performance but allows us to extract significant information on the quality of the approximated solution. Assuming that the underlying differential equation for the PINN training is an ordinary differential equation, we derive a rigorous upper limit on the PINN prediction error. This bound is applicable even for input data not included in the training phase and without any prior knowledge about the true solution. Therefore, our a posteriori error estimation is an essential step to certify the PINN. We apply our error estimator exemplarily to two academic toy problems, whereof one falls in the category of model-predictive control and thereby shows the practical use of the derived results.