Adequate uncertainty representation and quantification have become imperative in various scientific disciplines, especially in machine learning and artificial intelligence. As an alternative to representing uncertainty via one single probability measure, we consider credal sets (convex sets of probability measures). The geometric representation of credal sets as $d$-dimensional polytopes implies a geometric intuition about (epistemic) uncertainty. In this paper, we show that the volume of the geometric representation of a credal set is a meaningful measure of epistemic uncertainty in the case of binary classification, but less so for multi-class classification. Our theoretical findings highlight the crucial role of specifying and employing uncertainty measures in machine learning in an appropriate way, and for being aware of possible pitfalls.
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While deep neural network models offer unmatched classification performance, they are prone to learning spurious correlations in the data. Such dependencies on confounding information can be difficult to detect using performance metrics if the test data comes from the same distribution as the training data. Interpretable ML methods such as post-hoc explanations or inherently interpretable classifiers promise to identify faulty model reasoning. However, there is mixed evidence whether many of these techniques are actually able to do so. In this paper, we propose a rigorous evaluation strategy to assess an explanation technique's ability to correctly identify spurious correlations. Using this strategy, we evaluate five post-hoc explanation techniques and one inherently interpretable method for their ability to detect three types of artificially added confounders in a chest x-ray diagnosis task. We find that the post-hoc technique SHAP, as well as the inherently interpretable Attri-Net provide the best performance and can be used to reliably identify faulty model behavior.
Over the past decade, a long line of research has investigated the distributed complexity landscape of locally checkable labeling (LCL) problems on bounded-degree graphs, culminating in an almost-complete classification on general graphs and a complete classification on trees. The latter states that, on bounded-degree trees, any LCL problem has deterministic \emph{worst-case} time complexity $O(1)$, $\Theta(\log^* n)$, $\Theta(\log n)$, or $\Theta(n^{1/k})$ for some positive integer $k$, and all of those complexity classes are nonempty. Moreover, randomness helps only for (some) problems with deterministic worst-case complexity $\Theta(\log n)$, and if randomness helps (asymptotically), then it helps exponentially. In this work, we study how many distributed rounds are needed \emph{on average per node} in order to solve an LCL problem on trees. We obtain a partial classification of the deterministic \emph{node-averaged} complexity landscape for LCL problems. As our main result, we show that every problem with worst-case round complexity $O(\log n)$ has deterministic node-averaged complexity $O(\log^* n)$. We further establish bounds on the node-averaged complexity of problems with worst-case complexity $\Theta(n^{1/k})$: we show that all these problems have node-averaged complexity $\widetilde{\Omega}(n^{1 / (2^k - 1)})$, and that this lower bound is tight for some problems.
How to identify those equivalent entities between knowledge graphs (KGs), which is called Entity Alignment (EA), is a long-standing challenge. So far, many methods have been proposed, with recent focus on leveraging Deep Learning to solve this problem. However, we observe that most of the efforts has been paid to having better representation of entities, rather than improving entity matching from the learned representations. In fact, how to efficiently infer the entity pairs from this similarity matrix, which is essentially a matching problem, has been largely ignored by the community. Motivated by this observation, we conduct an in-depth analysis on existing algorithms that are particularly designed for solving this matching problem, and propose a novel matching method, named Bidirectional Matching (BMat). Our extensive experimental results on public datasets indicate that there is currently no single silver bullet solution for EA. In other words, different classes of entity similarity estimation may require different matching algorithms to reach the best EA results for each class. We finally conclude that using PARIS, the state-of-the-art EA approach, with BMat gives the best combination in terms of EA performance and the algorithm's time and space complexity.
Learning algorithms that divide the data into batches are prevalent in many machine-learning applications, typically offering useful trade-offs between computational efficiency and performance. In this paper, we examine the benefits of batch-partitioning through the lens of a minimum-norm overparameterized linear regression model with isotropic Gaussian features. We suggest a natural small-batch version of the minimum-norm estimator, and derive an upper bound on its quadratic risk, showing it is inversely proportional to the noise level as well as to the overparameterization ratio, for the optimal choice of batch size. In contrast to minimum-norm, our estimator admits a stable risk behavior that is monotonically increasing in the overparameterization ratio, eliminating both the blowup at the interpolation point and the double-descent phenomenon. Interestingly, we observe that this implicit regularization offered by the batch partition is partially explained by feature overlap between the batches. Our bound is derived via a novel combination of techniques, in particular normal approximation in the Wasserstein metric of noisy projections over random subspaces.
When developing and managing microservice systems, practitioners suggest that each microservice should be owned by a particular team. In effect, there is only one team with the responsibility to manage a given service. Consequently, one developer should belong to only one team. This practice of "one-microservice-per-developer" is especially prevalent in large projects with an extensive development team. Based on the bazaar-style software development model of Open Source Projects, in which different programmers, like vendors at a bazaar, offer to help out developing different parts of the system, this article investigates whether we can observe the "one-microservice-per-developer" behavior, a strategy we assume anticipated within microservice based Open Source Projects. We conducted an empirical study among 38 microservice-based OS projects. Our findings indicate that the strategy is rarely respected by open-source developers except for projects that have dedicated DevOps teams.
Short-packet communications are applied to various scenarios where transmission covertness and reliability are crucial due to the open wireless medium and finite blocklength. Although intelligent reflection surface (IRS) has been widely utilized to enhance transmission covertness and reliability, the question of how many reflection elements at IRS are required remains unanswered, which is vital to system design and practical deployment. The inherent strong coupling exists between the transmission covertness and reliability by IRS, leading to the question of intractability. To address this issue, the detection error probability at the warder and its approximation are derived first to reveal the relation between covertness performance and the number of reflection elements. Besides, to evaluate the reliability performance of the system, the decoding error probability at the receiver is also derived. Subsequently, the asymptotic reliability performance in high covertness regimes is investigated, which provides theoretical predictions about the number of reflection elements at IRS required to achieve a decoding error probability close to 0 with given covertness requirements. Furthermore, Monte-Carlo simulations verify the accuracy of the derived results for detection (decoding) error probabilities and the validity of the theoretical predictions for reflection elements. Moreover, results show that more reflection elements are required to achieve high reliability with tighter covertness requirements, longer blocklength and higher transmission rates.
How Informative is the Approximation Error from Tensor Decomposition for Neural Network Compression?
Tensor decompositions have been successfully applied to compress neural networks. The compression algorithms using tensor decompositions commonly minimize the approximation error on the weights. Recent work assumes the approximation error on the weights is a proxy for the performance of the model to compress multiple layers and fine-tune the compressed model. Surprisingly, little research has systematically evaluated which approximation errors can be used to make choices regarding the layer, tensor decomposition method, and level of compression. To close this gap, we perform an experimental study to test if this assumption holds across different layers and types of decompositions, and what the effect of fine-tuning is. We include the approximation error on the features resulting from a compressed layer in our analysis to test if this provides a better proxy, as it explicitly takes the data into account. We find the approximation error on the weights has a positive correlation with the performance error, before as well as after fine-tuning. Basing the approximation error on the features does not improve the correlation significantly. While scaling the approximation error commonly is used to account for the different sizes of layers, the average correlation across layers is smaller than across all choices (i.e. layers, decompositions, and level of compression) before fine-tuning. When calculating the correlation across the different decompositions, the average rank correlation is larger than across all choices. This means multiple decompositions can be considered for compression and the approximation error can be used to choose between them.
In pace with developments in the research field of artificial intelligence, knowledge graphs (KGs) have attracted a surge of interest from both academia and industry. As a representation of semantic relations between entities, KGs have proven to be particularly relevant for natural language processing (NLP), experiencing a rapid spread and wide adoption within recent years. Given the increasing amount of research work in this area, several KG-related approaches have been surveyed in the NLP research community. However, a comprehensive study that categorizes established topics and reviews the maturity of individual research streams remains absent to this day. Contributing to closing this gap, we systematically analyzed 507 papers from the literature on KGs in NLP. Our survey encompasses a multifaceted review of tasks, research types, and contributions. As a result, we present a structured overview of the research landscape, provide a taxonomy of tasks, summarize our findings, and highlight directions for future work.
As soon as abstract mathematical computations were adapted to computation on digital computers, the problem of efficient representation, manipulation, and communication of the numerical values in those computations arose. Strongly related to the problem of numerical representation is the problem of quantization: in what manner should a set of continuous real-valued numbers be distributed over a fixed discrete set of numbers to minimize the number of bits required and also to maximize the accuracy of the attendant computations? This perennial problem of quantization is particularly relevant whenever memory and/or computational resources are severely restricted, and it has come to the forefront in recent years due to the remarkable performance of Neural Network models in computer vision, natural language processing, and related areas. Moving from floating-point representations to low-precision fixed integer values represented in four bits or less holds the potential to reduce the memory footprint and latency by a factor of 16x; and, in fact, reductions of 4x to 8x are often realized in practice in these applications. Thus, it is not surprising that quantization has emerged recently as an important and very active sub-area of research in the efficient implementation of computations associated with Neural Networks. In this article, we survey approaches to the problem of quantizing the numerical values in deep Neural Network computations, covering the advantages/disadvantages of current methods. With this survey and its organization, we hope to have presented a useful snapshot of the current research in quantization for Neural Networks and to have given an intelligent organization to ease the evaluation of future research in this area.
The LSTM network was proposed to overcome the difficulty in learning long-term dependence, and has made significant advancements in applications. With its success and drawbacks in mind, this paper raises the question - do RNN and LSTM have long memory? We answer it partially by proving that RNN and LSTM do not have long memory from a statistical perspective. A new definition for long memory networks is further introduced, and it requires the model weights to decay at a polynomial rate. To verify our theory, we convert RNN and LSTM into long memory networks by making a minimal modification, and their superiority is illustrated in modeling long-term dependence of various datasets.
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