Inputs to machine learning models can have associated noise or uncertainties, but they are often ignored and not modelled. It is unknown if Bayesian Neural Networks and their approximations are able to consider uncertainty in their inputs. In this paper we build a two input Bayesian Neural Network (mean and standard deviation) and evaluate its capabilities for input uncertainty estimation across different methods like Ensembles, MC-Dropout, and Flipout. Our results indicate that only some uncertainty estimation methods for approximate Bayesian NNs can model input uncertainty, in particular Ensembles and Flipout.

This paper presents a new hybrid model for predicting German electricity prices. The algorithm is based on combining Gaussian Process Regression (GPR) and Support Vector Regression (SVR). While GPR is a competent model for learning the stochastic pattern within the data and interpolation, its performance for out-of-sample data is not very promising. By choosing a suitable data-dependent covariance function, we can enhance the performance of GPR for the tested German hourly power prices. However, since the out-of-sample prediction depends on the training data, the prediction is vulnerable to noise and outliers. To overcome this issue, a separate prediction is made using SVR, which applies margin-based optimization, having an advantage in dealing with non-linear processes and outliers, since only certain necessary points (support vectors) in the training data are responsible for regression. Both individual predictions are later combined using the performance-based weight assignment method. A test on historic German power prices shows that this approach outperforms its chosen benchmarks such as the autoregressive exogenous model, the naive approach, as well as the long short-term memory approach of prediction.

We study the differences arising from merging predictors in the causal and anticausal directions using the same data. In particular we study the asymmetries that arise in a simple model where we merge the predictors using one binary variable as target and two continuous variables as predictors. We use Causal Maximum Entropy (CMAXENT) as inductive bias to merge the predictors, however, we expect similar differences to hold also when we use other merging methods that take into account asymmetries between cause and effect. We show that if we observe all bivariate distributions, the CMAXENT solution reduces to a logistic regression in the causal direction and Linear Discriminant Analysis (LDA) in the anticausal direction. Furthermore, we study how the decision boundaries of these two solutions differ whenever we observe only some of the bivariate distributions implications for Out-Of-Variable (OOV) generalisation.

Across the scientific realm, we find ourselves subtracting or dividing stochastic signals. For instance, consider a stochastic realization, $x$, generated from the addition or multiplication of two stochastic signals $a$ and $b$, namely $x=a+b$ or $x = ab$. For the $x=a+b$ example, $a$ can be fluorescence background and $b$ the signal of interest whose statistics are to be learned from the measured $x$. Similarly, when writing $x=ab$, $a$ can be thought of as the illumination intensity and $b$ the density of fluorescent molecules of interest. Yet dividing or subtracting stochastic signals amplifies noise, and we ask instead whether, using the statistics of $a$ and the measurement of $x$ as input, we can recover the statistics of $b$. Here, we show how normalizing flows can generate an approximation of the probability distribution over $b$, thereby avoiding subtraction or division altogether. This method is implemented in our software package, NFdeconvolve, available on GitHub with a tutorial linked in the main text.

We observe that BatchBALD, a popular acquisition function for batch Bayesian active learning for classification, can conflate epistemic and aleatoric uncertainty, leading to suboptimal performance. Motivated by this observation, we propose to focus on the predictive probabilities, which only exhibit epistemic uncertainty. The result is an acquisition function that not only performs better, but is also faster to evaluate, allowing for larger batches than before.

Human Activity Recognition (HAR) has gained significant importance with the growing use of sensor-equipped devices and large datasets. This paper evaluates the performance of three categories of models : classical machine learning, deep learning architectures, and Restricted Boltzmann Machines (RBMs) using five key benchmark datasets of HAR (UCI-HAR, OPPORTUNITY, PAMAP2, WISDM, and Berkeley MHAD). We assess various models, including Decision Trees, Random Forests, Convolutional Neural Networks (CNN), and Deep Belief Networks (DBNs), using metrics such as accuracy, precision, recall, and F1-score for a comprehensive comparison. The results show that CNN models offer superior performance across all datasets, especially on the Berkeley MHAD. Classical models like Random Forest do well on smaller datasets but face challenges with larger, more complex data. RBM-based models also show notable potential, particularly for feature learning. This paper offers a detailed comparison to help researchers choose the most suitable model for HAR tasks.

The tree-width of a multivariate polynomial is the tree-width of the hypergraph with hyperedges corresponding to its terms. Multivariate polynomials of bounded tree-width have been studied by Makowsky and Meer as a new sparsity condition that allows for polynomial solvability of problems which are intractable in general. We consider a variation on this theme for Boolean variables. A representation of a Boolean function as the sign of a polynomial is called a polynomial threshold representation. We discuss Boolean functions representable as polynomial threshold functions of bounded tree-width and present two applications to Bayesian network classifiers, a probabilistic graphical model. Both applications are in Explainable Artificial Intelligence (XAI), the research area dealing with the black-box nature of many recent machine learning models. We also give a separation result between the representational power of positive and general polynomial threshold functions.

In this paper we provide a new efficient algorithm for approximately computing the profile maximum likelihood (PML) distribution, a prominent quantity in symmetric property estimation. We provide an algorithm which matches the previous best known efficient algorithms for computing approximate PML distributions and improves when the number of distinct observed frequencies in the given instance is small. We achieve this result by exploiting new sparsity structure in approximate PML distributions and providing a new matrix rounding algorithm, of independent interest. Leveraging this result, we obtain the first provable computationally efficient implementation of PseudoPML, a general framework for estimating a broad class of symmetric properties. Additionally, we obtain efficient PML-based estimators for distributions with small profile entropy, a natural instance-based complexity measure.

We describe two Monte Carlo algorithms for sampling from the integrated posterior distributions of a range of Bayesian mixture models. Both algorithms allow us to directly sample not only the assignment of observations to components but also the number of components, thereby fitting the model and performing model selection over the number of components in a single computation. The first algorithm is a traditional collapsed Gibbs sampler, albeit with an unusual move-set; the second builds on the first, adding rejection-free sampling from the prior over component assignments, to create an algorithm that has excellent mixing time in typical applications and outperforms current state-of-the-art methods, in some cases by a wide margin. We demonstrate our methods with a selection of applications to latent class analysis.

The emergence of large pre-trained vision-language models (VLMs) represents a paradigm shift in machine learning, with unprecedented results in a broad span of visual recognition tasks. CLIP, one of the most popular VLMs, has exhibited remarkable zero-shot and transfer learning capabilities in classification. To transfer CLIP to downstream tasks, adapters constitute a parameter-efficient approach that avoids backpropagation through the large model (unlike related prompt learning methods). However, CLIP adapters have been developed to target discriminative performance, and the quality of their uncertainty estimates has been overlooked. In this work we show that the discriminative performance of state-of-the-art CLIP adapters does not always correlate with their uncertainty estimation capabilities, which are essential for a safe deployment in real-world scenarios. We also demonstrate that one of such adapters is obtained through MAP inference from a more general probabilistic framework. Based on this observation we introduce BayesAdapter, which leverages Bayesian inference to estimate a full probability distribution instead of a single point, better capturing the variability inherent in the parameter space. In a comprehensive empirical evaluation we show that our approach obtains high quality uncertainty estimates in the predictions, standing out in calibration and selective classification. Our code will be publicly available upon acceptance of the paper.