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This paper describes a purely functional library for computing level-$p$-complexity of Boolean functions, and applies it to two-level iterated majority. Boolean functions are simply functions from $n$ bits to one bit, and they can describe digital circuits, voting systems, etc. An example of a Boolean function is majority, which returns the value that has majority among the $n$ input bits for odd $n$. The complexity of a Boolean function $f$ measures the cost of evaluating it: how many bits of the input are needed to be certain about the result of $f$. There are many competing complexity measures but we focus on level-$p$-complexity -- a function of the probability $p$ that a bit is 1. The level-$p$-complexity $D_p(f)$ is the minimum expected cost when the input bits are independent and identically distributed with Bernoulli($p$) distribution. We specify the problem as choosing the minimum expected cost of all possible decision trees -- which directly translates to a clearly correct, but very inefficient implementation. The library uses thinning and memoization for efficiency and type classes for separation of concerns. The complexity is represented using polynomials, and the order relation used for thinning is implemented using polynomial factorisation and root-counting. Finally we compute the complexity for two-level iterated majority and improve on an earlier result by J.~Jansson.

In recent years, learning-based feature detection and matching have outperformed manually-designed methods in in-air cases. However, it is challenging to learn the features in the underwater scenario due to the absence of annotated underwater datasets. This paper proposes a cross-modal knowledge distillation framework for training an underwater feature detection and matching network (UFEN). In particular, we use in-air RGBD data to generate synthetic underwater images based on a physical underwater imaging formation model and employ these as the medium to distil knowledge from a teacher model SuperPoint pretrained on in-air images. We embed UFEN into the ORB-SLAM3 framework to replace the ORB feature by introducing an additional binarization layer. To test the effectiveness of our method, we built a new underwater dataset with groundtruth measurements named EASI (//github.com/Jinghe-mel/UFEN-SLAM), recorded in an indoor water tank for different turbidity levels. The experimental results on the existing dataset and our new dataset demonstrate the effectiveness of our method.

Multiple systems estimation is a standard approach to quantifying hidden populations where data sources are based on lists of known cases. A typical modelling approach is to fit a Poisson loglinear model to the numbers of cases observed in each possible combination of the lists. It is necessary to decide which interaction parameters to include in the model, and information criterion approaches are often used for model selection. Difficulties in the context of multiple systems estimation may arise due to sparse or nil counts based on the intersection of lists, and care must be taken when information criterion approaches are used for model selection due to issues relating to the existence of estimates and identifiability of the model. Confidence intervals are often reported conditional on the model selected, providing an over-optimistic impression of the accuracy of the estimation. A bootstrap approach is a natural way to account for the model selection procedure. However, because the model selection step has to be carried out for every bootstrap replication, there may be a high or even prohibitive computational burden. We explore the merit of modifying the model selection procedure in the bootstrap to look only among a subset of models, chosen on the basis of their information criterion score on the original data. This provides large computational gains with little apparent effect on inference. Another model selection approach considered and investigated is a downhill search approach among models, possibly with multiple starting points.

Completely random measures (CRMs) provide a broad class of priors, arguably, the most popular, for Bayesian nonparametric (BNP) analysis of trait allocations. As a peculiar property, CRM priors lead to predictive distributions that share the following common structure: for fixed prior's parameters, a new data point exhibits a Poisson (random) number of ``new'' traits, i.e., not appearing in the sample, which depends on the sampling information only through the sample size. While the Poisson posterior distribution is appealing for analytical tractability and ease of interpretation, its independence from the sampling information is a critical drawback, as it makes the posterior distribution of ``new'' traits completely determined by the estimation of the unknown prior's parameters. In this paper, we introduce the class of transform-scaled process (T-SP) priors as a tool to enrich the posterior distribution of ``new'' traits arising from CRM priors, while maintaining the same analytical tractability and ease of interpretation. In particular, we present a framework for posterior analysis of trait allocations under T-SP priors, showing that Stable T-SP priors, i.e., T-SP priors built from Stable CRMs, lead to predictive distributions such that, for fixed prior's parameters, a new data point displays a negative-Binomial (random) number of ``new'' traits, which depends on the sampling information through the number of distinct traits and the sample size. Then, by relying on a hierarchical version of T-SP priors, we extend our analysis to the more general setting of trait allocations with multiple groups of data or subpopulations. The empirical effectiveness of our methods is demonstrated through numerical experiments and applications to real data.

The variety of complex algorithmic approaches for tackling time-series classification problems has grown considerably over the past decades, including the development of sophisticated but challenging-to-interpret deep-learning-based methods. But without comparison to simpler methods it can be difficult to determine when such complexity is required to obtain strong performance on a given problem. Here we evaluate the performance of an extremely simple classification approach -- a linear classifier in the space of two simple features that ignore the sequential ordering of the data: the mean and standard deviation of time-series values. Across a large repository of 128 univariate time-series classification problems, this simple distributional moment-based approach outperformed chance on 69 problems, and reached 100% accuracy on two problems. With a neuroimaging time-series case study, we find that a simple linear model based on the mean and standard deviation performs better at classifying individuals with schizophrenia than a model that additionally includes features of the time-series dynamics. Comparing the performance of simple distributional features of a time series provides important context for interpreting the performance of complex time-series classification models, which may not always be required to obtain high accuracy.

Balanced hypergraph partitioning is an NP-hard problem with many applications, e.g., optimizing communication in distributed data placement problems. The goal is to place all nodes across $k$ different blocks of bounded size, such that hyperedges span as few parts as possible. This problem is well-studied in sequential and distributed settings, but not in shared-memory. We close this gap by devising efficient and scalable shared-memory algorithms for all components employed in the best sequential solvers without compromises with regards to solution quality. This work presents the scalable and high-quality hypergraph partitioning framework Mt-KaHyPar. Its most important components are parallel improvement algorithms based on the FM algorithm and maximum flows, as well as a parallel clustering algorithm for coarsening - which are used in a multilevel scheme with $\log(n)$ levels. As additional components, we parallelize the $n$-level partitioning scheme, devise a deterministic version of our algorithm, and present optimizations for plain graphs. We evaluate our solver on more than 800 graphs and hypergraphs, and compare it with 25 different algorithms from the literature. Our fastest configuration outperforms almost all existing hypergraph partitioners with regards to both solution quality and running time. Our highest-quality configuration achieves the same solution quality as the best sequential partitioner KaHyPar, while being an order of magnitude faster with ten threads. Thus, two of our configurations occupy all fronts of the Pareto curve for hypergraph partitioning. Furthermore, our solvers exhibit good speedups, e.g., 29.6x in the geometric mean on 64 cores (deterministic), 22.3x ($\log(n)$-level), and 25.9x ($n$-level).

This paper focuses on the expected difference in borrower's repayment when there is a change in the lender's credit decisions. Classical estimators overlook the confounding effects and hence the estimation error can be magnificent. As such, we propose another approach to construct the estimators such that the error can be greatly reduced. The proposed estimators are shown to be unbiased, consistent, and robust through a combination of theoretical analysis and numerical testing. Moreover, we compare the power of estimating the causal quantities between the classical estimators and the proposed estimators. The comparison is tested across a wide range of models, including linear regression models, tree-based models, and neural network-based models, under different simulated datasets that exhibit different levels of causality, different degrees of nonlinearity, and different distributional properties. Most importantly, we apply our approaches to a large observational dataset provided by a global technology firm that operates in both the e-commerce and the lending business. We find that the relative reduction of estimation error is strikingly substantial if the causal effects are accounted for correctly.

Relation prediction for knowledge graphs aims at predicting missing relationships between entities. Despite the importance of inductive relation prediction, most previous works are limited to a transductive setting and cannot process previously unseen entities. The recent proposed subgraph-based relation reasoning models provided alternatives to predict links from the subgraph structure surrounding a candidate triplet inductively. However, we observe that these methods often neglect the directed nature of the extracted subgraph and weaken the role of relation information in the subgraph modeling. As a result, they fail to effectively handle the asymmetric/anti-symmetric triplets and produce insufficient embeddings for the target triplets. To this end, we introduce a \textbf{C}\textbf{o}mmunicative \textbf{M}essage \textbf{P}assing neural network for \textbf{I}nductive re\textbf{L}ation r\textbf{E}asoning, \textbf{CoMPILE}, that reasons over local directed subgraph structures and has a vigorous inductive bias to process entity-independent semantic relations. In contrast to existing models, CoMPILE strengthens the message interactions between edges and entitles through a communicative kernel and enables a sufficient flow of relation information. Moreover, we demonstrate that CoMPILE can naturally handle asymmetric/anti-symmetric relations without the need for explosively increasing the number of model parameters by extracting the directed enclosing subgraphs. Extensive experiments show substantial performance gains in comparison to state-of-the-art methods on commonly used benchmark datasets with variant inductive settings.

With the rapid increase of large-scale, real-world datasets, it becomes critical to address the problem of long-tailed data distribution (i.e., a few classes account for most of the data, while most classes are under-represented). Existing solutions typically adopt class re-balancing strategies such as re-sampling and re-weighting based on the number of observations for each class. In this work, we argue that as the number of samples increases, the additional benefit of a newly added data point will diminish. We introduce a novel theoretical framework to measure data overlap by associating with each sample a small neighboring region rather than a single point. The effective number of samples is defined as the volume of samples and can be calculated by a simple formula $(1-\beta^{n})/(1-\beta)$, where $n$ is the number of samples and $\beta \in [0,1)$ is a hyperparameter. We design a re-weighting scheme that uses the effective number of samples for each class to re-balance the loss, thereby yielding a class-balanced loss. Comprehensive experiments are conducted on artificially induced long-tailed CIFAR datasets and large-scale datasets including ImageNet and iNaturalist. Our results show that when trained with the proposed class-balanced loss, the network is able to achieve significant performance gains on long-tailed datasets.

We propose a new method for event extraction (EE) task based on an imitation learning framework, specifically, inverse reinforcement learning (IRL) via generative adversarial network (GAN). The GAN estimates proper rewards according to the difference between the actions committed by the expert (or ground truth) and the agent among complicated states in the environment. EE task benefits from these dynamic rewards because instances and labels yield to various extents of difficulty and the gains are expected to be diverse -- e.g., an ambiguous but correctly detected trigger or argument should receive high gains -- while the traditional RL models usually neglect such differences and pay equal attention on all instances. Moreover, our experiments also demonstrate that the proposed framework outperforms state-of-the-art methods, without explicit feature engineering.