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Signature-based techniques give mathematical insight into the interactions between complex streams of evolving data. These insights can be quite naturally translated into numerical approaches to understanding streamed data, and perhaps because of their mathematical precision, have proved useful in analysing streamed data in situations where the data is irregular, and not stationary, and the dimension of the data and the sample sizes are both moderate. Understanding streamed multi-modal data is exponential: a word in $n$ letters from an alphabet of size $d$ can be any one of $d^n$ messages. Signatures remove the exponential amount of noise that arises from sampling irregularity, but an exponential amount of information still remain. This survey aims to stay in the domain where that exponential scaling can be managed directly. Scalability issues are an important challenge in many problems but would require another survey article and further ideas. This survey describes a range of contexts where the data sets are small enough to remove the possibility of massive machine learning, and the existence of small sets of context free and principled features can be used effectively. The mathematical nature of the tools can make their use intimidating to non-mathematicians. The examples presented in this article are intended to bridge this communication gap and provide tractable working examples drawn from the machine learning context. Notebooks are available online for several of these examples. This survey builds on the earlier paper of Ilya Chevryev and Andrey Kormilitzin which had broadly similar aims at an earlier point in the development of this machinery. This article illustrates how the theoretical insights offered by signatures are simply realised in the analysis of application data in a way that is largely agnostic to the data type.

We pioneer a new technique that allows us to prove a multitude of previously open simulations in QBF proof complexity. In particular, we show that extended QBF Frege p-simulates clausal proof systems such as IR-Calculus, IRM-Calculus, Long-Distance Q-Resolution, and Merge Resolution. These results are obtained by taking a technique of Beyersdorff et al. (JACM 2020) that turns strategy extraction into simulation and combining it with new local strategy extraction arguments. This approach leads to simulations that are carried out mainly in propositional logic, with minimal use of the QBF rules. Our proofs therefore provide a new, largely propositional interpretation of the simulated systems. We argue that these results strengthen the case for uniform certification in QBF solving, since many QBF proof systems now fall into place underneath extended QBF Frege.

We study the discrete bin covering problem where a multiset of items from a fixed set $S \subseteq (0,1]$ must be split into disjoint subsets while maximizing the number of subsets whose contents sum to at least $1$. We study the online discrete variant, where $S$ is finite, and items arrive sequentially. In the purely online setting, we show that the competitive ratios of best deterministic (and randomized) algorithms converge to $\frac{1}{2}$ for large $S$, similar to the continuous setting. Therefore, we consider the problem under the prediction setting, where algorithms may access a vector of frequencies predicting the frequency of items of each size in the instance. In this setting, we introduce a family of online algorithms that perform near-optimally when the predictions are correct. Further, we introduce a second family of more robust algorithms that presents a tradeoff between the performance guarantees when the predictions are perfect and when predictions are adversarial. Finally, we consider a stochastic setting where items are drawn independently from any fixed but unknown distribution of $S$. Using results from the PAC-learnability of probabilities in discrete distributions, we also introduce a purely online algorithm whose average-case performance is near-optimal with high probability for all finite sets $S$ and all distributions of $S$.

It is well known that it is impossible to construct useful confidence intervals (CIs) about the mean or median of a response $Y$ conditional on features $X = x$ without making strong assumptions about the joint distribution of $X$ and $Y$. This paper introduces a new framework for reasoning about problems of this kind by casting the conditional problem at different levels of resolution, ranging from coarse to fine localization. In each of these problems, we consider local quantiles defined as the marginal quantiles of $Y$ when $(X,Y)$ is resampled in such a way that samples $X$ near $x$ are up-weighted while the conditional distribution $Y \mid X$ does not change. We then introduce the Weighted Quantile method, which asymptotically produces the uniformly most accurate confidence intervals for these local quantiles no matter the (unknown) underlying distribution. Another method, namely, the Quantile Rejection method, achieves finite sample validity under no assumption whatsoever. We conduct extensive numerical studies demonstrating that both of these methods are valid. In particular, we show that the Weighted Quantile procedure achieves nominal coverage as soon as the effective sample size is in the range of 10 to 20.

Omnidirectional stereo matching (OSM) is an essential and reliable means for $360^{\circ}$ depth sensing. However, following earlier works on conventional stereo matching, prior state-of-the-art (SOTA) methods rely on a 3D encoder-decoder block to regularize the cost volume, causing the whole system complicated and sub-optimal results. Recently, the Recurrent All-pairs Field Transforms (RAFT) based approach employs the recurrent update in 2D and has efficiently improved image-matching tasks, ie, optical flow, and stereo matching. To bridge the gap between OSM and RAFT, we mainly propose an opposite adaptive weighting scheme to seamlessly transform the outputs of spherical sweeping of OSM into the required inputs for the recurrent update, thus creating a recurrent omnidirectional stereo matching (RomniStereo) algorithm. Furthermore, we introduce two techniques, ie, grid embedding and adaptive context feature generation, which also contribute to RomniStereo's performance. Our best model improves the average MAE metric by 40.7\% over the previous SOTA baseline across five datasets. When visualizing the results, our models demonstrate clear advantages on both synthetic and realistic examples. The code is available at \url{//github.com/HalleyJiang/RomniStereo}.

Social relations are leveraged to tackle the sparsity issue of user-item interaction data in recommendation under the assumption of social homophily. However, social recommendation paradigms predominantly focus on homophily based on user preferences. While social information can enhance recommendations, its alignment with user preferences is not guaranteed, thereby posing the risk of introducing informational redundancy. We empirically discover that social graphs in real recommendation data exhibit low preference-aware homophily, which limits the effect of social recommendation models. To comprehensively extract preference-aware homophily information latent in the social graph, we propose Social Heterophily-alleviating Rewiring (SHaRe), a data-centric framework for enhancing existing graph-based social recommendation models. We adopt Graph Rewiring technique to capture and add highly homophilic social relations, and cut low homophilic (or heterophilic) relations. To better refine the user representations from reliable social relations, we integrate a contrastive learning method into the training of SHaRe, aiming to calibrate the user representations for enhancing the result of Graph Rewiring. Experiments on real-world datasets show that the proposed framework not only exhibits enhanced performances across varying homophily ratios but also improves the performance of existing state-of-the-art (SOTA) social recommendation models.

Previous work has highlighted that existing post-hoc explanation methods exhibit disparities in explanation fidelity (across 'race' and 'gender' as sensitive attributes), and while a large body of work focuses on mitigating these issues at the explanation metric level, the role of the data generating process and black box model in relation to explanation disparities remains largely unexplored. Accordingly, through both simulations as well as experiments on a real-world dataset, we specifically assess challenges to explanation disparities that originate from properties of the data: limited sample size, covariate shift, concept shift, omitted variable bias, and challenges based on model properties: inclusion of the sensitive attribute and appropriate functional form. Through controlled simulation analyses, our study demonstrates that increased covariate shift, concept shift, and omission of covariates increase explanation disparities, with the effect pronounced higher for neural network models that are better able to capture the underlying functional form in comparison to linear models. We also observe consistent findings regarding the effect of concept shift and omitted variable bias on explanation disparities in the Adult income dataset. Overall, results indicate that disparities in model explanations can also depend on data and model properties. Based on this systematic investigation, we provide recommendations for the design of explanation methods that mitigate undesirable disparities.

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.

Graph anomaly detection (GAD) is a challenging binary classification problem due to its different structural distribution between anomalies and normal nodes -- abnormal nodes are a minority, therefore holding high heterophily and low homophily compared to normal nodes. Furthermore, due to various time factors and the annotation preferences of human experts, the heterophily and homophily can change across training and testing data, which is called structural distribution shift (SDS) in this paper. The mainstream methods are built on graph neural networks (GNNs), benefiting the classification of normals from aggregating homophilous neighbors, yet ignoring the SDS issue for anomalies and suffering from poor generalization. This work solves the problem from a feature view. We observe that the degree of SDS varies between anomalies and normal nodes. Hence to address the issue, the key lies in resisting high heterophily for anomalies meanwhile benefiting the learning of normals from homophily. We tease out the anomaly features on which we constrain to mitigate the effect of heterophilous neighbors and make them invariant. We term our proposed framework as Graph Decomposition Network (GDN). Extensive experiments are conducted on two benchmark datasets, and the proposed framework achieves a remarkable performance boost in GAD, especially in an SDS environment where anomalies have largely different structural distribution across training and testing environments. Codes are open-sourced in //github.com/blacksingular/wsdm_GDN.

Blockchains deploy Transaction Fee Mechanisms (TFMs) to determine which user transactions to include in blocks and determine their payments (i.e., transaction fees). Increasing demand and scarce block resources have led to high user transaction fees. As these blockchains are a public resource, it may be preferable to reduce these transaction fees. To this end, we introduce Transaction Fee Redistribution Mechanisms (TFRMs) -- redistributing VCG payments collected from such TFM as rebates to minimize transaction fees. Classic redistribution mechanisms (RMs) achieve this while ensuring Allocative Efficiency (AE) and User Incentive Compatibility (UIC). Our first result shows the non-triviality of applying RM in TFMs. More concretely, we prove that it is impossible to reduce transaction fees when (i) transactions that are not confirmed do not receive rebates and (ii) the miner can strategically manipulate the mechanism. Driven by this, we propose \emph{Robust} TFRM (\textsf{R-TFRM}): a mechanism that compromises on an honest miner's individual rationality to guarantee strictly positive rebates to the users. We then introduce \emph{robust} and \emph{rational} TFRM (\textsf{R}$^2$\textsf{-TFRM}) that uses trusted on-chain randomness that additionally guarantees miner's individual rationality (in expectation) and strictly positive rebates. Our results show that TFRMs provide a promising new direction for reducing transaction fees in public blockchains.