A drawback of the classic approach for complexity analysis of distributed graph problems is that it mostly informs about the complexity of notorious classes of ``worst case'' graphs. Algorithms that are used to prove a tight (existential) bound are essentially optimized to perform well on such worst case graphs. However, such graphs are often either unlikely or actively avoided in practice, where benign graph instances usually admit much faster solutions. To circumnavigate these drawbacks, the concept of universal complexity analysis in the distributed setting was suggested by [Kutten and Peleg, PODC'95] and actively pursued by [Haeupler et al., STOC'21]. Here, the aim is to gauge the complexity of a distributed graph problem depending on the given graph instance. The challenge is to identify and understand the graph property that allows to accurately quantify the complexity of a distributed problem on a given graph. In the present work, we consider distributed shortest paths problems in the HYBRID model of distributed computing, where nodes have simultaneous access to two different modes of communication: one is restricted by locality and the other is restricted by congestion. We identify the graph parameter of neighborhood quality and show that it accurately describes a universal bound for the complexity of certain class of shortest paths problems in the HYBRID model.
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The impressive performance of recent language models across a wide range of tasks suggests that they possess a degree of abstract reasoning skills. Are these skills general and transferable, or specialized to specific tasks seen during pretraining? To disentangle these effects, we propose an evaluation framework based on "counterfactual" task variants that deviate from the default assumptions underlying standard tasks. Across a suite of 11 tasks, we observe nontrivial performance on the counterfactual variants, but nevertheless find that performance substantially and consistently degrades compared to the default conditions. This suggests that while current LMs may possess abstract task-solving skills to a degree, they often also rely on narrow, non-transferable procedures for task-solving. These results motivate a more careful interpretation of language model performance that teases apart these aspects of behavior.
One advantage of neural ranking models is that they are meant to generalise well in situations of synonymity i.e. where two words have similar or identical meanings. In this paper, we investigate and quantify how well various ranking models perform in a clear-cut case of synonymity: when words are simply expressed in different surface forms due to regional differences in spelling conventions (e.g., color vs colour). We first explore the prevalence of American and British English spelling conventions in datasets used for the pre-training, training and evaluation of neural retrieval methods, and find that American spelling conventions are far more prevalent. Despite these biases in the training data, we find that retrieval models often generalise well in this case of synonymity. We explore the effect of document spelling normalisation in retrieval and observe that all models are affected by normalising the document's spelling. While they all experience a drop in performance when normalised to a different spelling convention than that of the query, we observe varied behaviour when the document is normalised to share the query spelling convention: lexical models show improvements, dense retrievers remain unaffected, and re-rankers exhibit contradictory behaviour.
Although there is a huge literature on feature selection for the Cox model, none of the existing approaches can control the false discovery rate (FDR) unless the sample size tends to infinity. In addition, there is no formal power analysis of the knockoffs framework for survival data in the literature. To address those issues, in this paper, we propose a novel controlled feature selection approach using knockoffs for the Cox model. We establish that the proposed method enjoys the FDR control in finite samples regardless of the number of covariates. Moreover, under mild regularity conditions, we also show that the power of our method is asymptotically one as sample size tends to infinity. To the best of our knowledge, this is the first formal theoretical result on the power for the knockoffs procedure in the survival setting. Simulation studies confirm that our method has appealing finite-sample performance with desired FDR control and high power. We further demonstrate the performance of our method through a real data example.
Variable selection or importance measurement of input variables to a machine learning model has become the focus of much research. It is no longer enough to have a good model, one also must explain its decisions. This is why there are so many intelligibility algorithms available today. Among them, Shapley value estimation algorithms are intelligibility methods based on cooperative game theory. In the case of the naive Bayes classifier, and to our knowledge, there is no ``analytical" formulation of Shapley values. This article proposes an exact analytic expression of Shapley values in the special case of the naive Bayes Classifier. We analytically compare this Shapley proposal, to another frequently used indicator, the Weight of Evidence (WoE) and provide an empirical comparison of our proposal with (i) the WoE and (ii) KernelShap results on real world datasets, discussing similar and dissimilar results. The results show that our Shapley proposal for the naive Bayes classifier provides informative results with low algorithmic complexity so that it can be used on very large datasets with extremely low computation time.
To achieve the highest perceptual quality, state-of-the-art diffusion models are optimized with objectives that look very different from the maximum likelihood and the Evidence Lower Bound (ELBO) objectives. In this work, we reveal that diffusion model objectives are actually closely related to the ELBO. Specifically, we show that all commonly used diffusion model objectives equate to a weighted integral of ELBOs over different noise levels, where the weighting depends on the specific objective used. Under the condition of monotonic weighting, the connection is even closer: the diffusion objective then equals the ELBO, combined with simple data augmentation, namely Gaussian noise perturbation. We show that this condition holds for a number of state-of-the-art diffusion models. In experiments, we explore new monotonic weightings and demonstrate their effectiveness, achieving state-of-the-art FID scores on the high-resolution ImageNet benchmark.
A geometric graph is an abstract graph along with an embedding of the graph into the Euclidean plane which can be used to model a wide range of data sets. The ability to compare and cluster such objects is required in a data analysis pipeline, leading to a need for distances or metrics on these objects. In this work, we study the interleaving distance on geometric graphs, where functor representations of data can be compared by finding pairs of natural transformations between them. However, in many cases, particularly those of the set-valued functor variety, computation of the interleaving distance is NP-hard. For this reason, we take inspiration from the work of Robinson to find quality measures for families of maps that do not rise to the level of a natural transformation. Specifically, we call collections $\phi = \{\phi_U\mid U\}$ and $\psi = \{\psi_U\mid U\}$ which do not necessarily form a true interleaving an \textit{assignment}. In the case of embedded graphs, we impose a grid structure on the plane, treat this as a poset endowed with the Alexandroff topology $K$, and encode the embedded graph data as functors $F: \mathbf{Open}(K) \to \mathbf{Set}$ where $F(U)$ is the set of connected components of the graph inside of the geometric realization of the set $U$. We then endow the image with the extra structure of a metric space and define a loss function $L(\phi,\psi)$ which measures how far the required diagrams of an interleaving are from commuting. Then for a pair of assignments, we use this loss function to bound the interleaving distance, with an eye toward computation and approximation of the distance. We expect these ideas are not only useful in our particular use case of embedded graphs, but can be extended to a larger class of interleaving distance problems where computational complexity creates a barrier to use in practice.
We address the task of automatically scoring the competency of candidates based on textual features, from the automatic speech recognition (ASR) transcriptions in the asynchronous video job interview (AVI). The key challenge is how to construct the dependency relation between questions and answers, and conduct the semantic level interaction for each question-answer (QA) pair. However, most of the recent studies in AVI focus on how to represent questions and answers better, but ignore the dependency information and interaction between them, which is critical for QA evaluation. In this work, we propose a Hierarchical Reasoning Graph Neural Network (HRGNN) for the automatic assessment of question-answer pairs. Specifically, we construct a sentence-level relational graph neural network to capture the dependency information of sentences in or between the question and the answer. Based on these graphs, we employ a semantic-level reasoning graph attention network to model the interaction states of the current QA session. Finally, we propose a gated recurrent unit encoder to represent the temporal question-answer pairs for the final prediction. Empirical results conducted on CHNAT (a real-world dataset) validate that our proposed model significantly outperforms text-matching based benchmark models. Ablation studies and experimental results with 10 random seeds also show the effectiveness and stability of our models.
We propose a novel method for automatic reasoning on knowledge graphs based on debate dynamics. The main idea is to frame the task of triple classification as a debate game between two reinforcement learning agents which extract arguments -- paths in the knowledge graph -- with the goal to promote the fact being true (thesis) or the fact being false (antithesis), respectively. Based on these arguments, a binary classifier, called the judge, decides whether the fact is true or false. The two agents can be considered as sparse, adversarial feature generators that present interpretable evidence for either the thesis or the antithesis. In contrast to other black-box methods, the arguments allow users to get an understanding of the decision of the judge. Since the focus of this work is to create an explainable method that maintains a competitive predictive accuracy, we benchmark our method on the triple classification and link prediction task. Thereby, we find that our method outperforms several baselines on the benchmark datasets FB15k-237, WN18RR, and Hetionet. We also conduct a survey and find that the extracted arguments are informative for users.
Textual entailment is a fundamental task in natural language processing. Most approaches for solving the problem use only the textual content present in training data. A few approaches have shown that information from external knowledge sources like knowledge graphs (KGs) can add value, in addition to the textual content, by providing background knowledge that may be critical for a task. However, the proposed models do not fully exploit the information in the usually large and noisy KGs, and it is not clear how it can be effectively encoded to be useful for entailment. We present an approach that complements text-based entailment models with information from KGs by (1) using Personalized PageR- ank to generate contextual subgraphs with reduced noise and (2) encoding these subgraphs using graph convolutional networks to capture KG structure. Our technique extends the capability of text models exploiting structural and semantic information found in KGs. We evaluate our approach on multiple textual entailment datasets and show that the use of external knowledge helps improve prediction accuracy. This is particularly evident in the challenging BreakingNLI dataset, where we see an absolute improvement of 5-20% over multiple text-based entailment models.
We examine the problem of question answering over knowledge graphs, focusing on simple questions that can be answered by the lookup of a single fact. Adopting a straightforward decomposition of the problem into entity detection, entity linking, relation prediction, and evidence combination, we explore simple yet strong baselines. On the popular SimpleQuestions dataset, we find that basic LSTMs and GRUs plus a few heuristics yield accuracies that approach the state of the art, and techniques that do not use neural networks also perform reasonably well. These results show that gains from sophisticated deep learning techniques proposed in the literature are quite modest and that some previous models exhibit unnecessary complexity.
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