Models of choice are a fundamental input to many now-canonical optimization problems in the field of Operations Management, including assortment, inventory, and price optimization. Naturally, accurate estimation of these models from data is a critical step in the application of these optimization problems in practice. Concurrently, recent advancements in deep learning have sparked interest in integrating these techniques into choice modeling. However, there is a noticeable research gap at the intersection of deep learning and choice modeling, particularly with both theoretical and empirical foundations. Thus motivated, we first propose a choice model that is the first to successfully (both theoretically and practically) leverage a modern neural network architectural concept (self-attention). Theoretically, we show that our attention-based choice model is a low-rank generalization of the Halo Multinomial Logit (Halo-MNL) model. We prove that whereas the Halo-MNL requires $\Omega(m^2)$ data samples to estimate, where $m$ is the number of products, our model supports a natural nonconvex estimator (in particular, that which a standard neural network implementation would apply) which admits a near-optimal stationary point with $O(m)$ samples. Additionally, we establish the first realistic-scale benchmark for choice model estimation on real data, conducting the most extensive evaluation of existing models to date, thereby highlighting our model's superior performance.
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ACM/IEEE第23屆模型驅動工程語言和系統國際會議，是模型驅動軟件和系統工程的首要會議系列，由ACM-SIGSOFT和IEEE-TCSE支持組織。自1998年以來，模型涵蓋了建模的各個方面，從語言和方法到工具和應用程序。模特的參加者來自不同的背景，包括研究人員、學者、工程師和工業專業人士。MODELS 2019是一個論壇，參與者可以圍繞建模和模型驅動的軟件和系統交流前沿研究成果和創新實踐經驗。今年的版本將為建模社區提供進一步推進建模基礎的機會，并在網絡物理系統、嵌入式系統、社會技術系統、云計算、大數據、機器學習、安全、開源等新興領域提出建模的創新應用以及可持續性。
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We consider a family of two-valued "fully evaluated left-sequential logics" (FELs), of which Free FEL (defined by Staudt in 2012) is most distinguishing (weakest) and immune to atomic side effects. Next is Memorising FEL, in which evaluations of subexpressions are memorised. The following stronger logic is Conditional FEL (inspired by Guzm\'an and Squier's Conditional logic, 1990). The strongest FEL is static FEL, a sequential version of propositional logic. We use evaluation trees as a simple, intuitive semantics and provide complete axiomatisations for closed terms (left-sequential propositional expressions). For each FEL except Static FEL, we also define its three-valued version, with a constant U for "undefinedness" and again provide complete, independent aziomatisations, each one containing two additional axioms for U on top of the axiomatisations of the two-valued case. In this setting, the strongest FEL is equivalent to Bochvar's strict logic.
Time-optimal obstacle avoidance is a prevalent problem encountered in various fields, including robotics and autonomous vehicles, where the task involves determining a path for a moving vehicle to reach its goal while navigating around obstacles within its environment. This problem becomes increasingly challenging as the number of obstacles in the environment rises. We propose an iterative active-inactive obstacle approach, which involves identifying a subset of the obstacles as "active", that considers solely the effect of the "active" obstacles on the path of the moving vehicle. The remaining obstacles are considered "inactive" and are not considered in the path planning process. The obstacles are classified as 'active' on the basis of previous findings derived from prior iterations. This approach allows for a more efficient calculation of the optimal path by reducing the number of obstacles that need to be considered. The effectiveness of the proposed method is demonstrated with two different dynamic models using the various number of obstacles. The results show that the proposed method is able to find the optimal path in a timely manner, while also being able to handle a large number of obstacles in the environment and the constraints on the motion of the object.
The interactive theorem prover, Lean, enables the verification of formal mathematical proofs and is backed by an expanding community. Central to this ecosystem is its mathematical library, mathlib4, which lays the groundwork for the formalization of an expanding range of mathematical theories. However, searching for theorems in mathlib4 can be challenging. To successfully search in mathlib4, users often need to be familiar with its naming conventions or documentation strings. Therefore, creating a semantic search engine that can be used easily by individuals with varying familiarity with mathlib4 is very important. In this paper, we present a semantic search engine for mathlib4 that accepts informal queries and finds the relevant theorems. We also establish a benchmark for assessing the performance of various search engines for mathlib4.
As part of the activities of the IEEE-GDL CCD working group of physical infrastructure, this whitepaper is intented to be an initial guide to understand the layers, taxonomy of services and best practices for the development of smart buildings. Open standards are claimed in order to increase interoperability between layers and services. Moreover, two buildings in Guadalajara city, one new and another to renew, are described as a proof of concept under development and being part of the strategy to develop the smart city infrastructure based in a master plan. A discussion will be addressed in order to identify the areas of innovation and opportunities for the smart buildings as the contribution of this document.
When analysing Differentially Private (DP) machine learning pipelines, the potential privacy cost of data-dependent pre-processing is frequently overlooked in privacy accounting. In this work, we propose a general framework to evaluate the additional privacy cost incurred by non-private data-dependent pre-processing algorithms. Our framework establishes upper bounds on the overall privacy guarantees by utilising two new technical notions: a variant of DP termed Smooth DP and the bounded sensitivity of the pre-processing algorithms. In addition to the generic framework, we provide explicit overall privacy guarantees for multiple data-dependent pre-processing algorithms, such as data imputation, quantization, deduplication and PCA, when used in combination with several DP algorithms. Notably, this framework is also simple to implement, allowing direct integration into existing DP pipelines.
Decentralized Gradient Descent (DGD) is a popular algorithm used to solve decentralized optimization problems in diverse domains such as remote sensing, distributed inference, multi-agent coordination, and federated learning. Yet, executing DGD over wireless systems affected by noise, fading and limited bandwidth presents challenges, requiring scheduling of transmissions to mitigate interference and the acquisition of topology and channel state information -- complex tasks in wireless decentralized systems. This paper proposes a DGD algorithm tailored to wireless systems. Unlike existing approaches, it operates without inter-agent coordination, topology information, or channel state information. Its core is a Non-Coherent Over-The-Air (NCOTA) consensus scheme, exploiting a noisy energy superposition property of wireless channels. With a randomized transmission strategy to accommodate half-duplex operation, transmitters map local optimization signals to energy levels across subcarriers in an OFDM frame, and transmit concurrently without coordination. It is shown that received energies form a noisy consensus signal, whose fluctuations are mitigated via a consensus stepsize. NCOTA-DGD leverages the channel pathloss for consensus formation, without explicit knowledge of the mixing weights. It is shown that, for the class of strongly-convex problems, the expected squared distance between the local and globally optimum models vanishes with rate $\mathcal O(1/\sqrt{k})$ after $k$ iterations, with a proper design of decreasing stepsizes. Extensions address a broad class of fading models and frequency-selective channels. Numerical results on an image classification task depict faster convergence vis-\`a-vis running time than state-of-the-art schemes, especially in densely deployed networks.
Electromagnetic information theory (EIT) is one of the important topics for 6G communication due to its potential to reveal the performance limit of wireless communication systems. For EIT, the research foundation is reasonable and accurate channel modeling. Existing channel modeling works for EIT in non-line-of-sight (NLoS) scenario focus on far-field modeling, which can not accurately capture the characteristics of the channel in near-field. In this paper, we propose the near-field channel model for EIT based on electromagnetic scattering theory. We model the channel by using non-stationary Gaussian random fields and derive the analytical expression of the correlation function of the fields. Furthermore, we analyze the characteristics of the proposed channel model, e.g., the sparsity of the model in wavenumber domain. Based on the sparsity of the model, we design a channel estimation scheme for near-field scenario. Numerical analysis verifies the correctness of the proposed scheme and shows that it can outperform existing schemes like least square (LS) and orthogonal matching pursuit (OMP).
Large-scale machine learning problems make the cost of hyperparameter tuning ever more prohibitive. This creates a need for algorithms that can tune themselves on-the-fly. We formalize the notion of "tuning-free" algorithms that can match the performance of optimally-tuned optimization algorithms up to polylogarithmic factors given only loose hints on the relevant problem parameters. We consider in particular algorithms that can match optimally-tuned Stochastic Gradient Descent (SGD). When the domain of optimization is bounded, we show tuning-free matching of SGD is possible and achieved by several existing algorithms. We prove that for the task of minimizing a convex and smooth or Lipschitz function over an unbounded domain, tuning-free optimization is impossible. We discuss conditions under which tuning-free optimization is possible even over unbounded domains. In particular, we show that the recently proposed DoG and DoWG algorithms are tuning-free when the noise distribution is sufficiently well-behaved. For the task of finding a stationary point of a smooth and potentially nonconvex function, we give a variant of SGD that matches the best-known high-probability convergence rate for tuned SGD at only an additional polylogarithmic cost. However, we also give an impossibility result that shows no algorithm can hope to match the optimal expected convergence rate for tuned SGD with high probability.
The inductive biases of graph representation learning algorithms are often encoded in the background geometry of their embedding space. In this paper, we show that general directed graphs can be effectively represented by an embedding model that combines three components: a pseudo-Riemannian metric structure, a non-trivial global topology, and a unique likelihood function that explicitly incorporates a preferred direction in embedding space. We demonstrate the representational capabilities of this method by applying it to the task of link prediction on a series of synthetic and real directed graphs from natural language applications and biology. In particular, we show that low-dimensional cylindrical Minkowski and anti-de Sitter spacetimes can produce equal or better graph representations than curved Riemannian manifolds of higher dimensions.
Multi-relation Question Answering is a challenging task, due to the requirement of elaborated analysis on questions and reasoning over multiple fact triples in knowledge base. In this paper, we present a novel model called Interpretable Reasoning Network that employs an interpretable, hop-by-hop reasoning process for question answering. The model dynamically decides which part of an input question should be analyzed at each hop; predicts a relation that corresponds to the current parsed results; utilizes the predicted relation to update the question representation and the state of the reasoning process; and then drives the next-hop reasoning. Experiments show that our model yields state-of-the-art results on two datasets. More interestingly, the model can offer traceable and observable intermediate predictions for reasoning analysis and failure diagnosis.
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