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Many industrial and engineering processes monitored as times series have smooth trends that indicate normal behavior and occasionally anomalous patterns that can indicate a problem. This kind of behavior can be modeled by a smooth trend such as a spline or Gaussian process and a disruption based on a sparser representation. Our approach is to expand the process signal into two sets of basis functions: one set uses $L_2$ penalties on the coefficients and the other set uses $L_1$ penalties to control sparsity. From a frequentist perspective, this results in a hybrid smoother that combines cubic smoothing splines and the LASSO, and as a Bayesian hierarchical model (BHM), this is equivalent to priors giving a Gaussian process and a Laplace distribution for anomaly coefficients. For the hybrid smoother we propose two new ways of determining the penalty parameters that use effective degrees of freedom and contrast this with the BHM that uses loosely informative inverse gamma priors. Several reformulations are used to make sampling the BHM posterior more efficient including some novel features in orthogonalizing and regularizing the model basis functions. This methodology is motivated by a substantive application, monitoring the water treatment process for the Denver Metropolitan area. We also test the methods with a Monte Carlo study designed around the kind of anomalies expected in this application. Both the hybrid smoother and the full BHM give comparable results with small false positive and false negative rates. Besides being successful in the water treatment application, this work can be easily extended to other Gaussian process models and other features that represent process disruptions.

In social recommender systems, it is crucial that the recommendation models provide equitable visibility for different demographic groups, such as gender or race. Most existing research has addressed this problem by only studying individual static snapshots of networks that typically change over time. To address this gap, we study the evolution of recommendation fairness over time and its relation to dynamic network properties. We examine three real-world dynamic networks by evaluating the fairness of six recommendation algorithms and analyzing the association between fairness and network properties over time. We further study how interventions on network properties influence fairness by examining counterfactual scenarios with alternative evolution outcomes and differing network properties. Our results on empirical datasets suggest that recommendation fairness improves over time, regardless of the recommendation method. We also find that two network properties, minority ratio, and homophily ratio, exhibit stable correlations with fairness over time. Our counterfactual study further suggests that an extreme homophily ratio potentially contributes to unfair recommendations even with a balanced minority ratio. Our work provides insights into the evolution of fairness within dynamic networks in social science. We believe that our findings will help system operators and policymakers to better comprehend the implications of temporal changes and interventions targeting fairness in social networks.

We identify morphisms of strong profunctors as a categorification of quantum supermaps. These black-box generalisations of diagrams-with-holes are hence placed within the broader field of profunctor optics, as morphisms in the category of copresheaves on concrete networks. This enables the first construction of abstract logical connectives such as tensor products and negations for supermaps in a totally theory-independent setting. These logical connectives are found to be all that is needed to abstractly model the key structural features of the quantum theory of supermaps: black-box indefinite causal order, black-box definite causal order, and the factorisation of definitely causally ordered supermaps into concrete circuit diagrams. We demonstrate that at the heart of these factorisation theorems lies the Yoneda lemma and the notion of representability.

This paper considers the problem of constructing a confidence sequence, which is a sequence of confidence intervals that hold uniformly over time, for estimating the mean of bounded real-valued random processes. This paper revisits the gambling-based approach established in the recent literature from a natural \emph{two-horse race} perspective, and demonstrates new properties of the resulting algorithm induced by Cover (1991)'s universal portfolio. The main result of this paper is a new algorithm based on a mixture of lower bounds, which closely approximates the performance of Cover's universal portfolio with constant per-round time complexity. A higher-order generalization of a lower bound on a logarithmic function in (Fan et al., 2015), which is developed as a key technique for the proposed algorithm, may be of independent interest.

This paper is concerned with the problem of nonlinear filtering, i.e., computing the conditional distribution of the state of a stochastic dynamical system given a history of noisy partial observations. Conventional sequential importance resampling (SIR) particle filters suffer from fundamental limitations, in scenarios involving degenerate likelihoods or high-dimensional states, due to the weight degeneracy issue. In this paper, we explore an alternative method, which is based on estimating the Brenier optimal transport (OT) map from the current prior distribution of the state to the posterior distribution at the next time step. Unlike SIR particle filters, the OT formulation does not require the analytical form of the likelihood. Moreover, it allows us to harness the approximation power of neural networks to model complex and multi-modal distributions and employ stochastic optimization algorithms to enhance scalability. Extensive numerical experiments are presented that compare the OT method to the SIR particle filter and the ensemble Kalman filter, evaluating the performance in terms of sample efficiency, high-dimensional scalability, and the ability to capture complex and multi-modal distributions.

Emotion corpora are typically sampled based on keyword/hashtag search or by asking study participants to generate textual instances. In any case, these corpora are not uniform samples representing the entirety of a domain. We hypothesize that this practice of data acquisition leads to unrealistic correlations between overrepresented topics in these corpora that harm the generalizability of models. Such topic bias could lead to wrong predictions for instances like "I organized the service for my aunt's funeral." when funeral events are over-represented for instances labeled with sadness, despite the emotion of pride being more appropriate here. In this paper, we study this topic bias both from the data and the modeling perspective. We first label a set of emotion corpora automatically via topic modeling and show that emotions in fact correlate with specific topics. Further, we see that emotion classifiers are confounded by such topics. Finally, we show that the established debiasing method of adversarial correction via gradient reversal mitigates the issue. Our work points out issues with existing emotion corpora and that more representative resources are required for fair evaluation of models predicting affective concepts from text.

Document-level translation models are usually evaluated using general metrics such as BLEU, which are not informative about the benefits of context. Current work on context-aware evaluation, such as contrastive methods, only measure translation accuracy on words that need context for disambiguation. Such measures cannot reveal whether the translation model uses the correct supporting context. We propose to complement accuracy-based evaluation with measures of context utilization. We find that perturbation-based analysis (comparing models' performance when provided with correct versus random context) is an effective measure of overall context utilization. For a finer-grained phenomenon-specific evaluation, we propose to measure how much the supporting context contributes to handling context-dependent discourse phenomena. We show that automatically-annotated supporting context gives similar conclusions to human-annotated context and can be used as alternative for cases where human annotations are not available. Finally, we highlight the importance of using discourse-rich datasets when assessing context utilization.

Recent work introduced an algorithm and tool in Coq to automatically repair broken proofs in response to changes that correspond to type equivalences. We report on case studies for manual proof repair across type equivalences using an adaptation of this algorithm in Cubical Agda. Crucially, these case studies capture proof repair use cases that were challenging to impossible in prior work in Coq due to type theoretic limitations, highlighting three benefits to working in Cubical Agda: (1) quotient types enrich the space of repairs we can express as type equivalences, (2) dependent path equality makes it possible to internally state and prove correctness of repaired proofs relative to the original proofs, and (3) functional extensionality and transport make it simple to move between slow and fast computations after repair. They also highlight two challenges of working in Cubical Agda, namely those introduced by: (1) lack of tools for automation, and (2) proof relevance, especially as it interacts with definitional equality. We detail these benefits and challenges in hopes to set the stage for later work in proof repair bridging the benefits of both languages.

This paper serves as a survey of recent advances in large margin training and its theoretical foundations, mostly for (nonlinear) deep neural networks (DNNs) that are probably the most prominent machine learning models for large-scale data in the community over the past decade. We generalize the formulation of classification margins from classical research to latest DNNs, summarize theoretical connections between the margin, network generalization, and robustness, and introduce recent efforts in enlarging the margins for DNNs comprehensively. Since the viewpoint of different methods is discrepant, we categorize them into groups for ease of comparison and discussion in the paper. Hopefully, our discussions and overview inspire new research work in the community that aim to improve the performance of DNNs, and we also point to directions where the large margin principle can be verified to provide theoretical evidence why certain regularizations for DNNs function well in practice. We managed to shorten the paper such that the crucial spirit of large margin learning and related methods are better emphasized.

The notion of "in-domain data" in NLP is often over-simplistic and vague, as textual data varies in many nuanced linguistic aspects such as topic, style or level of formality. In addition, domain labels are many times unavailable, making it challenging to build domain-specific systems. We show that massive pre-trained language models implicitly learn sentence representations that cluster by domains without supervision -- suggesting a simple data-driven definition of domains in textual data. We harness this property and propose domain data selection methods based on such models, which require only a small set of in-domain monolingual data. We evaluate our data selection methods for neural machine translation across five diverse domains, where they outperform an established approach as measured by both BLEU and by precision and recall of sentence selection with respect to an oracle.