We describe a general approach for maximum a posteriori (MAP) inference in a class of discrete-continuous factor graphs commonly encountered in robotics applications. While there are openly available tools providing flexible and easy-to-use interfaces for specifying and solving inference problems formulated in terms of either discrete or continuous graphical models, at present, no similarly general tools exist enabling the same functionality for hybrid discrete-continuous problems. We aim to address this problem. In particular, we provide a library, DC-SAM, extending existing tools for inference problems defined in terms of factor graphs to the setting of discrete-continuous models. A key contribution of our work is a novel solver for efficiently recovering approximate solutions to discrete-continuous inference problems. The key insight to our approach is that while joint inference over continuous and discrete state spaces is often hard, many commonly encountered discrete-continuous problems can naturally be split into a "discrete part" and a "continuous part" that can individually be solved easily. Leveraging this structure, we optimize discrete and continuous variables in an alternating fashion. In consequence, our proposed work enables straightforward representation of and approximate inference in discrete-continuous graphical models. We also provide a method to approximate the uncertainty in estimates of both discrete and continuous variables. We demonstrate the versatility of our approach through its application to distinct robot perception applications, including robust pose graph optimization, and object-based mapping and localization.

The study of quasar light curves poses two problems: inference of the power spectrum and interpolation of an irregularly sampled time series. A baseline approach to these tasks is to interpolate a time series with a Damped Random Walk (DRW) model, in which the spectrum is inferred using Maximum Likelihood Estimation (MLE). However, the DRW model does not describe the smoothness of the time series, and MLE faces many problems in terms of optimization and numerical precision. In this work, we introduce a new stochastic model that we call $\textit{Convolved Damped Random Walk}$ (CDRW). This model introduces a concept of smoothness to a DRW, which enables it to describe quasar spectra completely. We also introduce a new method of inference of Gaussian process parameters, which we call $\textit{Neural Inference}$. This method uses the powers of state-of-the-art neural networks to improve the conventional MLE inference technique. In our experiments, the Neural Inference method results in significant improvement over the baseline MLE (RMSE: $0.318 \rightarrow 0.205$, $0.464 \rightarrow 0.444$). Moreover, the combination of both the CDRW model and Neural Inference significantly outperforms the baseline DRW and MLE in interpolating a typical quasar light curve ($\chi^2$: $0.333 \rightarrow 0.998$, $2.695 \rightarrow 0.981$). The code is published on GitHub.

Coadded astronomical images are created by stacking multiple single-exposure images. Because coadded images are smaller in terms of data size than the single-exposure images they summarize, loading and processing them is less computationally expensive. However, image coaddition introduces additional dependence among pixels, which complicates principled statistical analysis of them. We present a principled Bayesian approach for performing light source parameter inference with coadded astronomical images. Our method implicitly marginalizes over the single-exposure pixel intensities that contribute to the coadded images, giving it the computational efficiency necessary to scale to next-generation astronomical surveys. As a proof of concept, we show that our method for estimating the locations and fluxes of stars using simulated coadds outperforms a method trained on single-exposure images.

Active learning has been studied extensively as a method for efficient data collection. Among the many approaches in literature, Expected Error Reduction (EER) (Roy and McCallum) has been shown to be an effective method for active learning: select the candidate sample that, in expectation, maximally decreases the error on an unlabeled set. However, EER requires the model to be retrained for every candidate sample and thus has not been widely used for modern deep neural networks due to this large computational cost. In this paper we reformulate EER under the lens of Bayesian active learning and derive a computationally efficient version that can use any Bayesian parameter sampling method (such as arXiv:1506.02142). We then compare the empirical performance of our method using Monte Carlo dropout for parameter sampling against state of the art methods in the deep active learning literature. Experiments are performed on four standard benchmark datasets and three WILDS datasets (arXiv:2012.07421). The results indicate that our method outperforms all other methods except one in the data shift scenario: a model dependent, non-information theoretic method that requires an order of magnitude higher computational cost (arXiv:1906.03671).

Machine Learning involves algorithms that learn from patterns of data and then apply it to decision making. Deep Learning, on the other hand, is able to learn through processing data on its own and is quite similar to the human brain where it identifies something, analyse it, and makes a decision.

Artificial Neural Networks (ANNs) have been successfully used in various nuclear engineering applications, such as predicting reactor physics parameters within reasonable time and with a high level of accuracy. Despite this success, they cannot provide information about the model prediction uncertainties, making it difficult to assess ANN prediction credibility, especially in extrapolated domains. In this study, Deep Neural Networks (DNNs) are used to predict the assembly axial neutron flux profiles in the SAFARI-1 research reactor, with quantified uncertainties in the ANN predictions and extrapolation to cycles not used in the training process. The training dataset consists of copper-wire activation measurements, the axial measurement locations and the measured control bank positions obtained from the reactor's historical cycles. Uncertainty Quantification of the regular DNN models' predictions is performed using Monte Carlo Dropout (MCD) and Bayesian Neural Networks solved by Variational Inference (BNN VI). The regular DNNs, DNNs solved with MCD and BNN VI results agree very well among each other as well as with the new measured dataset not used in the training process, thus indicating good prediction and generalization capability. The uncertainty bands produced by MCD and BNN VI agree very well, and in general, they can fully envelop the noisy measurement data points. The developed ANNs are useful in supporting the experimental measurements campaign and neutronics code Verification and Validation (V&V).

Bayesian Networks may be appealing for clinical decision-making due to their inclusion of causal knowledge, but their practical adoption remains limited as a result of their inability to deal with unstructured data. While neural networks do not have this limitation, they are not interpretable and are inherently unable to deal with causal structure in the input space. Our goal is to build neural networks that combine the advantages of both approaches. Motivated by the perspective to inject causal knowledge while training such neural networks, this work presents initial steps in that direction. We demonstrate how a neural network can be trained to output conditional probabilities, providing approximately the same functionality as a Bayesian Network. Additionally, we propose two training strategies that allow encoding the independence relations inferred from a given causal structure into the neural network.

Direct Loss Minimization (DLM) has been proposed as a pseudo-Bayesian method motivated as regularized loss minimization. Compared to variational inference, it replaces the loss term in the evidence lower bound (ELBO) with the predictive log loss, which is the same loss function used in evaluation. A number of theoretical and empirical results in prior work suggest that DLM can significantly improve over ELBO optimization for some models. However, as we point out in this paper, this is not the case for Bayesian neural networks (BNNs). The paper explores the practical performance of DLM for BNN, the reasons for its failure and its relationship to optimizing the ELBO, uncovering some interesting facts about both algorithms.

Often the data that a model needs to be trained on is distributed among multiple computing agents and it cannot be accrued in a single server location because of logistical constraints such as memory, efficient data sharing means, or confidentiality requirements due to sensitive nature of the data. However, the need arises to train the same model with the entire distributed data. Isolated training individually by the agents with their local data may lead to overfitted models as the training data is limited. Besides, training such isolated models on different agents is redundant as more parameter updates have to be performed by the isolated models to reach a certain level of accuracy as compared to what can be achieved by sharing information. Distributed learning aims to leverage the full distributed data by a coordinated training among all the agents where the agents are allowed to share partial information (usually the learned model parameters or their gradients) without sharing any raw data.

In brain-computer interfaces (BCI), most of the approaches based on event-related potential (ERP) focus on the detection of P300, aiming for single trial classification for a speller task. While this is an important objective, existing P300 BCI still require several repetitions to achieve a correct classification accuracy. Signal processing and machine learning advances in P300 BCI mostly revolve around the P300 detection part, leaving the character classification out of the scope. To reduce the number of repetitions while maintaining a good character classification, it is critical to embrace the full classification problem. We introduce an end-to-end pipeline, starting from feature extraction, and is composed of an ERP-level classification using probabilistic Riemannian MDM which feeds a character-level classification using Bayesian accumulation of confidence across trials. Whereas existing approaches only increase the confidence of a character when it is flashed, our new pipeline, called Bayesian accumulation of Riemannian probabilities (ASAP), update the confidence of each character after each flash. We provide the proper derivation and theoretical reformulation of this Bayesian approach for a seamless processing of information from signal to BCI characters. We demonstrate that our approach performs significantly better than standard methods on public P300 datasets.