We study the problem of fair and efficient allocation of a set of indivisible goods to agents with additive valuations using the popular fairness notions of envy-freeness up to one good (EF1) and equitability up to one good (EQ1) in conjunction with Pareto-optimality (PO). There exists a pseudo-polynomial time algorithm to compute an EF1+PO allocation and a non-constructive proof of the existence of allocations that are both EF1 and fractionally Pareto-optimal (fPO), which is a stronger notion than PO. We present a pseudo-polynomial time algorithm to compute an EF1+fPO allocation, thereby improving the earlier results. Our techniques also enable us to show that an EQ1+fPO allocation always exists when the values are positive and that it can be computed in pseudo-polynomial time. We also consider the class of $k$-ary instances where $k$ is a constant, i.e., each agent has at most $k$ different values for the goods. For such instances, we show that an EF1+fPO allocation can be computed in strongly polynomial time. When all values are positive, we show that an EQ1+fPO allocation for such instances can be computed in strongly polynomial time. Next, we consider instances where the number of agents is constant and show that an EF1+PO (likewise, an EQ1+PO) allocation can be computed in polynomial time. These results significantly extend the polynomial-time computability beyond the known cases of binary or identical valuations. We also design a polynomial-time algorithm that computes a Nash welfare maximizing allocation when there are constantly many agents with constant many different values for the goods. Finally, on the complexity side, we show that the problem of computing an EF1+fPO allocation lies in the complexity class PLS.
Supervised learning methods have shown effectiveness in estimating spatial acoustic parameters such as time difference of arrival, direct-to-reverberant ratio and reverberation time. However, they still suffer from the simulation-to-reality generalization problem due to the mismatch between simulated and real-world acoustic characteristics and the deficiency of annotated real-world data. To this end, this work proposes a self-supervised method that takes full advantage of unlabeled data for spatial acoustic parameter estimation. First, a new pretext task, i.e. cross-channel signal reconstruction (CCSR), is designed to learn a universal spatial acoustic representation from unlabeled multi-channel microphone signals. We mask partial signals of one channel and ask the model to reconstruct them, which makes it possible to learn spatial acoustic information from unmasked signals and extract source information from the other microphone channel. An encoder-decoder structure is used to disentangle the two kinds of information. By fine-tuning the pre-trained spatial encoder with a small annotated dataset, this encoder can be used to estimate spatial acoustic parameters. Second, a novel multi-channel audio Conformer (MC-Conformer) is adopted as the encoder model architecture, which is suitable for both the pretext and downstream tasks. It is carefully designed to be able to capture the local and global characteristics of spatial acoustics exhibited in the time-frequency domain. Experimental results of five acoustic parameter estimation tasks on both simulated and real-world data show the effectiveness of the proposed method. To the best of our knowledge, this is the first self-supervised learning method in the field of spatial acoustic representation learning and multi-channel audio signal processing.
We study the scheduling problem in a status update system composed of an arbitrary number of information sources with different service time distributions and weights for the purpose of minimizing the weighted sum age of information (AoI). In particular, we study open-loop schedulers which rely only on the statistics (specifically, only on the first two moments) of the source service times, in contrast to closed-loop schedulers that also make use of the actual realizations of the service times and the AoI processes in making scheduling decisions. Open-loop scheduling policies can be constructed off-line and are simpler to implement compared to their closed-loop counterparts. We consider the generate-at-will (GAW) model, and develop an analytical method to calculate the exact AoI for the probabilistic and cyclic open-loop schedulers. In both cases, the server initiates the sampling of a source and the ensuing transmission of the update packet from the source to the server in an open-loop manner; either based on a certain probability (probabilistic scheme) or according to a deterministic cyclic pattern (cyclic scheme). We derive the optimum open-loop cyclic scheduling policy in closed form for the specific case of N=2 sources and propose well-performing heuristic cyclic schedulers for general number of sources, i.e., N>2. We study the proposed cyclic schedulers against probabilistic schedulers and several existing methods in the literature to validate their effectiveness.
Sonification research is intrinsically interdisciplinary. Consequently, a proper documentation of, and interdisciplinary discourse about a sonification is often hindered by terminology discrepancies between involved disciplines, i.e., the lack of a common sound terminology in sonification research. Without a common ground, a researcher from one discipline may have troubles understanding the implementation and imagining the resulting sound perception of a sonification, if the sonification is described by a researcher from another discipline. To find a common ground, I consulted literature on interdisciplinary research and discourse, identified problems that occur in sonification, and applied the recommended solutions. As a result, I recommend considering three aspects of sonification individually, namely 1.) Sound Design Concept, 2.) Objective and 3.) Method, clarifying which discipline is involved in which aspect, and sticking to this discipline's terminology. As two requirements of sonifications are that they are a) reproducible and b) interpretable, I recommend documenting and discussing every sonification design once using audio engineering terminology, and once using psychoacoustic terminology. The appendix provides comprehensive lists of sound terms from both disciplines, together with relevant literature and a clarification of often misunderstood and misused terms.
Off-Policy Evaluation (OPE) aims to assess the effectiveness of counterfactual policies using only offline logged data and is often used to identify the top-k promising policies for deployment in online A/B tests. Existing evaluation metrics for OPE estimators primarily focus on the "accuracy" of OPE or that of downstream policy selection, neglecting risk-return tradeoff in the subsequent online policy deployment. To address this issue, we draw inspiration from portfolio evaluation in finance and develop a new metric, called SharpeRatio@k, which measures the risk-return tradeoff of policy portfolios formed by an OPE estimator under varying online evaluation budgets (k). We validate our metric in two example scenarios, demonstrating its ability to effectively distinguish between low-risk and high-risk estimators and to accurately identify the most efficient estimator. This efficient estimator is characterized by its capability to form the most advantageous policy portfolios, maximizing returns while minimizing risks during online deployment, a nuance that existing metrics typically overlook. To facilitate a quick, accurate, and consistent evaluation of OPE via SharpeRatio@k, we have also integrated this metric into an open-source software, SCOPE-RL. Employing SharpeRatio@k and SCOPE-RL, we conduct comprehensive benchmarking experiments on various estimators and RL tasks, focusing on their risk-return tradeoff. These experiments offer several interesting directions and suggestions for future OPE research.
Achievability in information theory refers to demonstrating a coding strategy that accomplishes a prescribed performance benchmark for the underlying task. In quantum information theory, the crafted Hayashi-Nagaoka operator inequality is an essential technique in proving a wealth of one-shot achievability bounds since it effectively resembles a union bound in various problems. In this work, we show that the pretty-good measurement naturally plays a role as the union bound as well. A judicious application of it considerably simplifies the derivation of one-shot achievability for classical-quantum (c-q) channel coding via an elegant three-line proof. The proposed analysis enjoys the following favorable features. (i) The established one-shot bound admits a closed-form expression as in the celebrated Holevo-Helstrom Theorem. Namely, the error probability of sending $M$ messages through a c-q channel is upper bounded by the minimum error of distinguishing the joint channel input-output state against $(M-1)$ decoupled products states. (ii) Our bound directly yields asymptotic results in the large deviation, small deviation, and moderate deviation regimes in a unified manner. (iii) The coefficients incurred in applying the Hayashi-Nagaoka operator inequality are no longer needed. Hence, the derived one-shot bound sharpens existing results relying on the Hayashi-Nagaoka operator inequality. In particular, we obtain the tightest achievable $\epsilon$-one-shot capacity for c-q channel coding heretofore, improving the third-order coding rate in the asymptotic scenario. (iv) Our result holds for infinite-dimensional Hilbert space. (v) The proposed method applies to deriving one-shot achievability for classical data compression with quantum side information, entanglement-assisted classical communication over quantum channels, and various quantum network information-processing protocols.
Although robust statistical estimators are less affected by outlying observations, their computation is usually more challenging. This is particularly the case in high-dimensional sparse settings. The availability of new optimization procedures, mainly developed in the computer science domain, offers new possibilities for the field of robust statistics. This paper investigates how such procedures can be used for robust sparse association estimators. The problem can be split into a robust estimation step followed by an optimization for the remaining decoupled, (bi-)convex problem. A combination of the augmented Lagrangian algorithm and adaptive gradient descent is implemented to also include suitable constraints for inducing sparsity. We provide results concerning the precision of the algorithm and show the advantages over existing algorithms in this context. High-dimensional empirical examples underline the usefulness of this procedure. Extensions to other robust sparse estimators are possible.
We investigate the role of various demonstration components in the in-context learning (ICL) performance of large language models (LLMs). Specifically, we explore the impacts of ground-truth labels, input distribution, and complementary explanations, particularly when these are altered or perturbed. We build on previous work, which offers mixed findings on how these elements influence ICL. To probe these questions, we employ explainable NLP (XNLP) methods and utilize saliency maps of contrastive demonstrations for both qualitative and quantitative analysis. Our findings reveal that flipping ground-truth labels significantly affects the saliency, though it's more noticeable in larger LLMs. Our analysis of the input distribution at a granular level reveals that changing sentiment-indicative terms in a sentiment analysis task to neutral ones does not have as substantial an impact as altering ground-truth labels. Finally, we find that the effectiveness of complementary explanations in boosting ICL performance is task-dependent, with limited benefits seen in sentiment analysis tasks compared to symbolic reasoning tasks. These insights are critical for understanding the functionality of LLMs and guiding the development of effective demonstrations, which is increasingly relevant in light of the growing use of LLMs in applications such as ChatGPT. Our research code is publicly available at //github.com/paihengxu/XICL.
The fusion of causal models with deep learning introducing increasingly intricate data sets, such as the causal associations within images or between textual components, has surfaced as a focal research area. Nonetheless, the broadening of original causal concepts and theories to such complex, non-statistical data has been met with serious challenges. In response, our study proposes redefinitions of causal data into three distinct categories from the standpoint of causal structure and representation: definite data, semi-definite data, and indefinite data. Definite data chiefly pertains to statistical data used in conventional causal scenarios, while semi-definite data refers to a spectrum of data formats germane to deep learning, including time-series, images, text, and others. Indefinite data is an emergent research sphere inferred from the progression of data forms by us. To comprehensively present these three data paradigms, we elaborate on their formal definitions, differences manifested in datasets, resolution pathways, and development of research. We summarize key tasks and achievements pertaining to definite and semi-definite data from myriad research undertakings, present a roadmap for indefinite data, beginning with its current research conundrums. Lastly, we classify and scrutinize the key datasets presently utilized within these three paradigms.
We consider the problem of explaining the predictions of graph neural networks (GNNs), which otherwise are considered as black boxes. Existing methods invariably focus on explaining the importance of graph nodes or edges but ignore the substructures of graphs, which are more intuitive and human-intelligible. In this work, we propose a novel method, known as SubgraphX, to explain GNNs by identifying important subgraphs. Given a trained GNN model and an input graph, our SubgraphX explains its predictions by efficiently exploring different subgraphs with Monte Carlo tree search. To make the tree search more effective, we propose to use Shapley values as a measure of subgraph importance, which can also capture the interactions among different subgraphs. To expedite computations, we propose efficient approximation schemes to compute Shapley values for graph data. Our work represents the first attempt to explain GNNs via identifying subgraphs explicitly and directly. Experimental results show that our SubgraphX achieves significantly improved explanations, while keeping computations at a reasonable level.
This work considers the question of how convenient access to copious data impacts our ability to learn causal effects and relations. In what ways is learning causality in the era of big data different from -- or the same as -- the traditional one? To answer this question, this survey provides a comprehensive and structured review of both traditional and frontier methods in learning causality and relations along with the connections between causality and machine learning. This work points out on a case-by-case basis how big data facilitates, complicates, or motivates each approach.