An experimental comparison of two or more optimization algorithms requires the same computational resources to be assigned to each algorithm. When a maximum runtime is set as the stopping criterion, all algorithms need to be executed in the same machine if they are to use the same resources. Unfortunately, the implementation code of the algorithms is not always available, which means that running the algorithms to be compared in the same machine is not always possible. And even if they are available, some optimization algorithms might be costly to run, such as training large neural-networks in the cloud. In this paper, we consider the following problem: how do we compare the performance of a new optimization algorithm B with a known algorithm A in the literature if we only have the results (the objective values) and the runtime in each instance of algorithm A? Particularly, we present a methodology that enables a statistical analysis of the performance of algorithms executed in different machines. The proposed methodology has two parts. First, we propose a model that, given the runtime of an algorithm in a machine, estimates the runtime of the same algorithm in another machine. This model can be adjusted so that the probability of estimating a runtime longer than what it should be is arbitrarily low. Second, we introduce an adaptation of the one-sided sign test that uses a modified p-value and takes into account that probability. Such adaptation avoids increasing the probability of type I error associated with executing algorithms A and B in different machines.
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This paper addresses the problem of statistical inference for latent continuous-time stochastic processes, which is often intractable, particularly for discrete state space processes described by Markov jump processes. To overcome this issue, we propose a new tractable inference scheme based on an entropic matching framework that can be embedded into the well-known expectation propagation algorithm. We demonstrate the effectiveness of our method by providing closed-form results for a simple family of approximate distributions and apply it to the general class of chemical reaction networks, which are a crucial tool for modeling in systems biology. Moreover, we derive closed form expressions for point estimation of the underlying parameters using an approximate expectation maximization procedure. We evaluate the performance of our method on various chemical reaction network instantiations, including a stochastic Lotka-Voltera example, and discuss its limitations and potential for future improvements. Our proposed approach provides a promising direction for addressing complex continuous-time Bayesian inference problems.
Blockwise determinantal ideals are those generated by the union of all the minors of specified sizes in certain blocks of a generic matrix, and they are the natural generalization of many existing determinantal ideals like the Schubert and ladder ones. In this paper we establish several criteria to verify whether the Gr\"obner bases of blockwise determinantal ideals with respect to (anti-)diagonal term orders are minimal or reduced. In particular, for Schubert determinantal ideals, while all the elusive minors form the reduced Gr\"obner bases when the defining permutations are vexillary, in the non-vexillary case we derive an explicit formula for computing the reduced Gr\"obner basis from elusive minors which avoids all algebraic operations. The fundamental properties of being normal and strong for W-characteristic sets and characteristic pairs, which are heavily connected to the reduced Gr\"obner bases, of Schubert determinantal ideals are also proven.
The increasing demand for computational power in big data and machine learning has driven the development of distributed training methodologies. Among these, peer-to-peer (P2P) networks provide advantages such as enhanced scalability and fault tolerance. However, they also encounter challenges related to resource consumption, costs, and communication overhead as the number of participating peers grows. In this paper, we introduce a novel architecture that combines serverless computing with P2P networks for distributed training and present a method for efficient parallel gradient computation under resource constraints. Our findings show a significant enhancement in gradient computation time, with up to a 97.34\% improvement compared to conventional P2P distributed training methods. As for costs, our examination confirmed that the serverless architecture could incur higher expenses, reaching up to 5.4 times more than instance-based architectures. It is essential to consider that these higher costs are associated with marked improvements in computation time, particularly under resource-constrained scenarios. Despite the cost-time trade-off, the serverless approach still holds promise due to its pay-as-you-go model. Utilizing dynamic resource allocation, it enables faster training times and optimized resource utilization, making it a promising candidate for a wide range of machine learning applications.
The substitution lemma is a renowned theorem within the realm of lambda-calculus theory and concerns the interactional behaviour of the metasubstitution operation. In this work, we augment the lambda-calculus's grammar with an uninterpreted explicit substitution operator, which allows the use of our framework for different calculi with explicit substitutions. Our primary contribution lies in verifying that, despite these modifications, the substitution lemma continues to remain valid. This confirmation was achieved using the Coq proof assistant. Our formalization methodology employs a nominal approach, which provides a direct implementation of the alpha-equivalence concept. The strategy involved in variable renaming within the proofs presents a challenge, specially on ensuring an exploration of the implications of our extension to the grammar of the lambda-calculus.
6G promises a paradigm shift in which positioning and sensing are inherently integrated, enhancing not only the communication performance but also enabling location- and context-aware services. Historically, positioning and sensing have been viewed through the lens of cost and performance trade-offs, implying an escalated demand for resources, such as radio, physical, and computational resources, for improved performance. However, 6G goes beyond this traditional perspective to encompass a set of broader values, namely sustainability, inclusiveness, and trustworthiness. This paper aims to: (i) shed light on these important value indicators and their relationship with the conventional key performance indicators, and (ii) unveil the dual nature of 6G in relation to these key value indicators (i.e., ensuring operation according to the values and enabling services that affect the values).
Fractional (hyper-)graph theory is concerned with the specific problems that arise when fractional analogues of otherwise integer-valued (hyper-)graph invariants are considered. The focus of this paper is on fractional edge covers of hypergraphs. Our main technical result generalizes and unifies previous conditions under which the size of the support of fractional edge covers is bounded independently of the size of the hypergraph itself. This allows us to extend previous tractability results for checking if the fractional hypertree width of a given hypergraph is $\leq k$ for some constant $k$. We also show how our results translate to fractional vertex covers.
Prognostics and Health Management (PHM) is a discipline focused on predicting the point at which systems or components will cease to perform as intended, typically measured as Remaining Useful Life (RUL). RUL serves as a vital decision-making tool for contingency planning, guiding the timing and nature of system maintenance. Historically, PHM has primarily been applied to hardware systems, with its application to software only recently explored. In a recent study we introduced a methodology and demonstrated how changes in software can impact the RUL of software. However, in practical software development, real-time performance is also influenced by various environmental attributes, including operating systems, clock speed, processor performance, RAM, machine core count and others. This research extends the analysis to assess how changes in environmental attributes, such as operating system and clock speed, affect RUL estimation in software. Findings are rigorously validated using real performance data from controlled test beds and compared with predictive model-generated data. Statistical validation, including regression analysis, supports the credibility of the results. The controlled test bed environment replicates and validates faults from real applications, ensuring a standardized assessment platform. This exploration yields actionable knowledge for software maintenance and optimization strategies, addressing a significant gap in the field of software health management.
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.
We propose a novel approach to multimodal sentiment analysis using deep neural networks combining visual analysis and natural language processing. Our goal is different than the standard sentiment analysis goal of predicting whether a sentence expresses positive or negative sentiment; instead, we aim to infer the latent emotional state of the user. Thus, we focus on predicting the emotion word tags attached by users to their Tumblr posts, treating these as "self-reported emotions." We demonstrate that our multimodal model combining both text and image features outperforms separate models based solely on either images or text. Our model's results are interpretable, automatically yielding sensible word lists associated with emotions. We explore the structure of emotions implied by our model and compare it to what has been posited in the psychology literature, and validate our model on a set of images that have been used in psychology studies. Finally, our work also provides a useful tool for the growing academic study of images - both photographs and memes - on social networks.
While it is nearly effortless for humans to quickly assess the perceptual similarity between two images, the underlying processes are thought to be quite complex. Despite this, the most widely used perceptual metrics today, such as PSNR and SSIM, are simple, shallow functions, and fail to account for many nuances of human perception. Recently, the deep learning community has found that features of the VGG network trained on the ImageNet classification task has been remarkably useful as a training loss for image synthesis. But how perceptual are these so-called "perceptual losses"? What elements are critical for their success? To answer these questions, we introduce a new Full Reference Image Quality Assessment (FR-IQA) dataset of perceptual human judgments, orders of magnitude larger than previous datasets. We systematically evaluate deep features across different architectures and tasks and compare them with classic metrics. We find that deep features outperform all previous metrics by huge margins. More surprisingly, this result is not restricted to ImageNet-trained VGG features, but holds across different deep architectures and levels of supervision (supervised, self-supervised, or even unsupervised). Our results suggest that perceptual similarity is an emergent property shared across deep visual representations.
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