In this work, we consider a classification problem in unsupervised domain adaptation (UDA). UDA aims to transfer knowledge from a source domain with ample labeled data to enhance the performance in a target domain where labeled data is unavailable. In UDA, the source and target domains have different data generating distributions, so the core challenge is to transfer knowledge contained in the labeled dataset in the source domain to the target domain under the distribution shifts. Over the decades, significant improvements in the transferability from source to target domains have been made, resulting in areas like domain alignment (Ben-David et al., 2010; Ganin et al., 2016; Long et al., 2018; Zhang et al., 2019) and self-training (Cai et al., 2021; Chen et al., 2020; Liu et al., 2021). Improving calibration performance, which is about matching predictions regarding a random event to the long-term occurrence of the event (Dawid, 1982), is of central interest in the machine learning community due to its significance to safe and trustworthy deployment of machine learning models in critical real-world decision-making systems (Amodei et al., 2016; Lee and See, 2004). In independent and identically distributed (i.i.d.) settings, calibration performance has been significantly improved by various approaches (Gal and Ghahramani, 2016; Guo et al., 2017; Lakshminarayanan et al., 2017). However, producing well-calibrated predictions in UDA remains challenging due to the distribution shifts. Specifically, Wang et al. (2020) show the discernible compromise in calibration performance as an offset against the enhancement of target accuracy. A further observation reveals that state-of-the-art calibrated classifiers in the i.i.d.

Meta-learning has demonstrated promising results in few-shot classification (FSC) by learning to solve new problems using prior knowledge. Bayesian methods are effective at characterizing uncertainty in FSC, which is crucial in high-risk fields. In this context, the logistic-softmax likelihood is often employed as an alternative to the softmax likelihood in multi-class Gaussian process classification due to its conditional conjugacy property. However, the theoretical property of logistic-softmax is not clear and previous research indicated that the inherent uncertainty of logistic-softmax leads to suboptimal performance. To mitigate these issues, we revisit and redesign the logistic-softmax likelihood, which enables control of the \textit{a priori} confidence level through a temperature parameter. Furthermore, we theoretically and empirically show that softmax can be viewed as a special case of logistic-softmax and logistic-softmax induces a larger family of data distribution than softmax. Utilizing modified logistic-softmax, we integrate the data augmentation technique into the deep kernel based Gaussian process meta-learning framework, and derive an analytical mean-field approximation for task-specific updates. Our approach yields well-calibrated uncertainty estimates and achieves comparable or superior results on standard benchmark datasets. Code is publicly available at \url{https://github.com/keanson/revisit-logistic-softmax}.

Mutual information quantifies the dependence between two random variables and remains invariant under diffeomorphisms. In this paper, we explore the pointwise mutual information profile, an extension of mutual information that maintains this invariance. We analytically describe the profiles of multivariate normal distributions and introduce the family of fine distributions, for which the profile can be accurately approximated using Monte Carlo methods. We then show how fine distributions can be used to study the limitations of existing mutual information estimators, investigate the behavior of neural critics used in variational estimators, and understand the effect of experimental outliers on mutual information estimation. Finally, we show how fine distributions can be used to obtain model-based Bayesian estimates of mutual information, suitable for problems with available domain expertise in which uncertainty quantification is necessary.

The elusive nature of gradient-based optimization in neural networks is tied to their loss landscape geometry, which is poorly understood. However recent work has brought solid evidence that there is essentially no loss barrier between the local solutions of gradient descent, once accounting for weight-permutations that leave the network's computation unchanged. This raises questions for approximate inference in Bayesian neural networks (BNNs), where we are interested in marginalizing over multiple points in the loss landscape. In this work, we first extend the formalism of marginalized loss barrier and solution interpolation to BNNs, before proposing a matching algorithm to search for linearly connected solutions. This is achieved by aligning the distributions of two independent approximate Bayesian solutions with respect to permutation matrices. We build on the results of Ainsworth et al. (2023), reframing the problem as a combinatorial optimization one, using an approximation to the sum of bilinear assignment problem. We then experiment on a variety of architectures and datasets, finding nearly zero marginalized loss barriers for linearly connected solutions.

In structured prediction, target objects have rich internal structure which does not factorize into independent components and violates common i.i.d. assumptions. This challenge becomes apparent through the exponentially large output space in applications such as image segmentation or scene graph generation. We present a novel PAC-Bayesian risk bound for structured prediction wherein the rate of generalization scales not only with the number of structured examples but also with their size. The underlying assumption, conforming to ongoing research on generative models, is that data are generated by the Knothe-Rosenblatt rearrangement of a factorizing reference measure. This allows to explicitly distill the structure between random output variables into a Wasserstein dependency matrix. Our work makes a preliminary step towards leveraging powerful generative models to establish generalization bounds for discriminative downstream tasks in the challenging setting of structured prediction.

Large collections of time series data are often organized into hierarchies with different levels of aggregation; examples include product and geographical groupings. Probabilistic coherent forecasting is tasked to produce forecasts consistent across levels of aggregation. In this study, we propose to augment neural forecasting architectures with a coherent multivariate mixture output. We optimize the networks with a composite likelihood objective, allowing us to capture time series' relationships while maintaining high computational efficiency. Our approach demonstrates 13.2% average accuracy improvements on most datasets compared to state-of-the-art baselines. We conduct ablation studies of the framework components and provide theoretical foundations for them. To assist related work, the code is available at this https://github.com/Nixtla/neuralforecast.

While machine learning (ML) has made significant contributions to the biopharmaceutical field, its applications are still in the early stages in terms of providing direct support for quality-by-design based development and manufacturing of biopharmaceuticals, hindering the enormous potential for bioprocesses automation from their development to manufacturing. However, the adoption of ML-based models instead of conventional multivariate data analysis methods is significantly increasing due to the accumulation of large-scale production data. This trend is primarily driven by the real-time monitoring of process variables and quality attributes of biopharmaceutical products through the implementation of advanced process analytical technologies. Given the complexity and multidimensionality of a bioproduct design, bioprocess development, and product manufacturing data, ML-based approaches are increasingly being employed to achieve accurate, flexible, and high-performing predictive models to address the problems of analytics, monitoring, and control within the biopharma field. This paper aims to provide a comprehensive review of the current applications of ML solutions in a bioproduct design, monitoring, control, and optimisation of upstream, downstream, and product formulation processes. Finally, this paper thoroughly discusses the main challenges related to the bioprocesses themselves, process data, and the use of machine learning models in biopharmaceutical process development and manufacturing. Moreover, it offers further insights into the adoption of innovative machine learning methods and novel trends in the development of new digital biopharma solutions.

The core principle of Variational Inference (VI) is to convert the statistical inference problem of computing complex posterior probability densities into a tractable optimization problem. This property enables VI to be faster than several sampling-based techniques. However, the traditional VI algorithm is not scalable to large data sets and is unable to readily infer out-of-bounds data points without re-running the optimization process. Recent developments in the field, like stochastic-, black box-, and amortized-VI, have helped address these issues. Generative modeling tasks nowadays widely make use of amortized VI for its efficiency and scalability, as it utilizes a parameterized function to learn the approximate posterior density parameters. In this paper, we review the mathematical foundations of various VI techniques to form the basis for understanding amortized VI. Additionally, we provide an overview of the recent trends that address several issues of amortized VI, such as the amortization gap, generalization issues, inconsistent representation learning, and posterior collapse. Finally, we analyze alternate divergence measures that improve VI optimization.

The worst-case resource usage of a program can provide useful information for many software-engineering tasks, such as performance optimization and algorithmic-complexity-vulnerability discovery. This paper presents a generic, adaptive, and sound fuzzing framework, called DSE-SMC, for estimating worst-case resource usage. DSE-SMC is generic because it is black-box as long as the user provides an interface for retrieving resource-usage information on a given input; adaptive because it automatically balances between exploration and exploitation of candidate inputs; and sound because it is guaranteed to converge to the true resource-usage distribution of the analyzed program. DSE-SMC is built upon a key observation: resource accumulation in a program is isomorphic to the soft-conditioning mechanism in Bayesian probabilistic programming; thus, worst-case resource analysis is isomorphic to the maximum-a-posteriori-estimation problem of Bayesian statistics. DSE-SMC incorporates sequential Monte Carlo (SMC) -- a generic framework for Bayesian inference -- with adaptive evolutionary fuzzing algorithms, in a sound manner, i.e., DSE-SMC asymptotically converges to the posterior distribution induced by resource-usage behavior of the analyzed program. Experimental evaluation on Java applications demonstrates that DSE-SMC is significantly more effective than existing black-box fuzzing methods for worst-case analysis.

We introduce a univariate signal deconvolution method based on the principles of an approach to Artificial General Intelligence in order to build a general-purpose model of models independent of any arbitrarily assumed prior probability distribution. We investigate how non-random data may encode information about the physical properties, such as dimensions and length scales of the space in which a signal or message may have been originally encoded, embedded, or generated. Our multidimensional space reconstruction method is based on information theory and algorithmic probability, so that it is proven to be agnostic vis-a-vis the arbitrarily chosen encoding-decoding scheme, computable or semi-computable method of approximation to algorithmic complexity, and computational model. The results presented in this paper are useful for applications in coding theory, particularly in zero-knowledge one-way communication channels, such as in deciphering messages from unknown generating sources about which no prior knowledge is available and to which no return message can be sent. We argue that this method has the potential to be of great value in cryptography, signal processing, causal deconvolution, life and technosignature detection.