Answering complex queries in store fulfillment, such as ''What percentage of employee-assigned actions remain unresolved?'' or ''How many worklists for a specific product type were completed within a timeframe at each location?'' requires precise, multi-hop reasoning across datasets with varying granularities. This paper introduces an ontology-based knowledge graph (KG) approach integrated with a structured text-to-Cypher generation pipeline, enabling accurate retrieval for such queries. Benchmarking against a robust hybrid search baseline combining BM25 and semantic search, our method demonstrates superior performance in addressing multi-hop and cross-granularity questions. Leveraging a KG schema designed to capture intricate relationships (e.g. (OrderLineItem)-[:INVOLVES_ACTION]->(Action)-[:INVOLVES]->(BatchProcess)-[:IS_COMPLETED_AT]->(Location)), we reveal universal patterns for constructing and querying highly relational data. This work highlights the transformative potential of ontology-driven KGs to improve reasoning, data aggregation, and decision-making, with broader implications for any domain requiring structured, multi-relational data analysis.

Emerging applications of machine learning in numerous areas-including online social networks, remote sensing, Internet-of-Things (IoT) systems, smart grids, and more-involve continuous gathering of and learning from streams of data samples. Real-time incorporation of streaming data into the learned machine learning models is essential for improved inference in these applications. Furthermore, these applications often involve data that are either inherently gathered at geographically distributed entities due to physical reasons, for example, IoT systems and smart grids, or that are intentionally distributed across multiple computing machines for memory, storage, computational, and/or privacy reasons. Training of machine learning models in this distributed, streaming setting requires solving stochastic optimization (SO) problems in a collaborative manner over communication links between the physical entities. When the streaming data rate is high compared with the processing capabilities of individual computing entities and/or the rate of the communications links, this poses a challenging question: How can one best leverage the incoming data for distributed training of machine learning models under constraints on computing capabilities and/or communications rate? A large body of research in distributed online optimization has emerged in recent decades to tackle this and related problems. This article reviews recently developed methods that focus on large-scale distributed SO in the compute- and bandwidth-limited regimes, with an emphasis on convergence analysis that explicitly accounts for the mismatch between computation, communication, and streaming rates and provides sufficient conditions for order-optimum convergence. In particular, it focuses on methods that solve: 1) distributed stochastic convex problems and 2) distributed principal component analysis, which is a nonconvex problem with the geometric structure that permits global convergence. For such methods, this article discusses recent advances in terms of distributed algorithmic designs when faced with high-rate streaming data. Furthermore, it reviews theoretical guarantees underlying these methods that show that there exist regimes in which systems can learn from distributed processing of streaming data at order-optimal rates-nearly as fast as if all the data were processed at a single superpowerful machine.

We consider the problem of detecting whether a tensor signal having many missing entities lies within a given low dimensional Kronecker-Structured (KS) subspace. This is a matched subspace detection problem. Tensor matched subspace detection problem is more challenging because of the intertwined signal dimensions. We solve this problem by projecting the signal onto the KS subspace, which is a Kronecker product of different subspaces corresponding to each signal dimension. Under this framework, we define the KS subspaces and the orthogonal projection of the signal onto the KS subspace. We prove that reliable detection is possible as long as the cardinality of the missing signal is greater than the dimensions of the KS subspace by bounding the residual energy of the sampling signal with high probability.

Multi-scale spectrum sensing is proposed to overcome the cost of full network state information on the spectrum occupancy of primary users (PUs) in dense multi-cell cognitive networks. Secondary users (SUs) estimate the local spectrum occupancies and aggregate them hierarchically to estimate spectrum occupancy at multiple spatial scales. Thus, SUs obtain fine-grained estimates of spectrum occupancies of nearby cells, more relevant to scheduling tasks, and coarse-grained estimates of those of distant cells. An agglomerative clustering algorithm is proposed to design a cost-effective aggregation tree, matched to the structure of interference, robust to local estimation errors, and delays. Given these multi-scale estimates, the SU traffic is adapted in a decentralized fashion in each cell, to optimize the trade-off among SU cell throughput, interference caused to PUs, and mutual SU interference. Numerical evaluations demonstrate a small degradation in SU cell throughput (up to 15% for a 0 dB interference-to-noise ratio experienced at PUs) compared to a scheme with full network state information, using only one-third of the cost incurred in the exchange of spectrum estimates. The proposed interference-matched design is shown to significantly outperform a random tree design, by providing more relevant information for network control, and a state-of-the-art consensus-based algorithm, which does not leverage the spatio-temporal structure of interference across the network.

In this paper, we develop a reinforcement learning (RL) based system to learn an effective policy for carpooling that maximizes transportation efficiency so that fewer cars are required to fulfill the given amount of trip demand. For this purpose, first, we develop a deep neural network model, called ST-NN (Spatio-Temporal Neural Network), to predict taxi trip time from the raw GPS trip data. Secondly, we develop a carpooling simulation environment for RL training, with the output of ST-NN and using the NYC taxi trip dataset. In order to maximize transportation efficiency and minimize traffic congestion, we choose the effective distance covered by the driver on a carpool trip as the reward. Therefore, the more effective distance a driver achieves over a trip (i.e. to satisfy more trip demand) the higher the efficiency and the less will be the traffic congestion. We compared the performance of RL learned policy to a fixed policy (which always accepts carpool) as a baseline and obtained promising results that are interpretable and demonstrate the advantage of our RL approach. We also compare the performance of ST-NN to that of state-of-the-art travel time estimation methods and observe that ST-NN significantly improves the prediction performance and is more robust to outliers.

In this paper, a multi-scale approach to spectrum sensing in cognitive cellular networks is proposed. In order to overcome the huge cost incurred in the acquisition of full network state information, a hierarchical scheme is proposed, based on which local state estimates are aggregated up the hierarchy to obtain aggregate state information at multiple scales, which are then sent back to each cell for local decision making. Thus, each cell obtains fine-grained estimates of the channel occupancies of nearby cells, but coarse-grained estimates of those of distant cells. The performance of the aggregation scheme is studied in terms of the trade-off between the throughput achievable by secondary users and the interference generated by the activity of these secondary users to primary users. In order to account for the irregular structure of interference patterns arising from path loss, shadowing, and blockages, which are especially relevant in millimeter wave networks, a greedy algorithm is proposed to find a multi-scale aggregation tree to optimize the performance. It is shown numerically that this tailored hierarchy outperforms a regular tree construction by 60%.

Kronecker-structured (K-S) models have been proposed for the efficient representation, processing, and classification of multidimensional signals such as images and video. In this paper, we study the classification performance of Kronecker-structured models in two asymptotic regimes. First, we study the diversity order, the slope of the error probability as the signal noise power goes to zero. We derive an exact expression for the diversity order as a function of the signal and subspace dimensions of a K-S model. Next, we study the classification capacity, the maximum rate at which the number of classes can grow as the signal dimension goes to infinity. We derive upper and lower bounds on the prelog factor of the classification capacity. Finally, we evaluate the empirical classification performance of K-S models, showing that they agree with the diversity order analysis.

Large datasets often have unreliable labels-such as those obtained from Amazon's Mechanical Turk or social media platforms-and classifiers trained on mislabeled datasets often exhibit poor performance. We present a simple, effective technique for accounting for label noise when training deep neural networks. We augment a standard deep network with a softmax layer that models the label noise statistics. Then, we train the deep network and noise model jointly via end-to-end stochastic gradient descent on the (perhaps mislabeled) dataset. The augmented model is underdetermined, so in order to encourage the learning of a non-trivial noise model, we apply dropout regularization to the weights of the noise model during training. Numerical experiments on noisy versions of the CIFAR-10 and MNIST datasets show that the proposed dropout technique outperforms state-of-the-art methods.

This paper proposes a low-complexity scheme to construct Voronoi constellations for the shaping of high-dimensional lattice codes. The Voronoi region of a low-dimensional lattice is used as a prototype for the shaping region for a high-dimensional lattice codebook. The proposed scheme retains the shaping and coding gains of the respective lattices. Further, the proposed scheme provides a general approach for shaping popular high-dimensional lattices, including LDA lattices, for which no practical shaping algorithm exists to our knowledge. Finally, the proposed scheme preserves the algebraic properties of nested lattice codes, making it suitable for compute-and-forward applications. Using E8and BW16as prototype shaping lattices, we numerically show that the proposed scheme results in 0:65 dB and 0:86 dB shaping gains.

An information-theoretic framework is presented for estimating the number of labeled samples needed to train a classifier in a parametric Bayesian setting. Ideas from rate-distortion theory are used to derive bounds for the average L1or L∞distance between the learned classifier and the true maximum a posteriori classifier in terms of familiar information-theoretic quantities and the number of training samples available. The maximum a posteriori classifier is viewed as a random source, labeled training data are viewed as a finite-rate encoding of the source, and the L1or L∞Bayes risk is viewed as the average distortion. The result is a framework dual to the well-known probably approximately correct (PAC) framework. PAC bounds characterize worst-case learning performance of a family of classifiers whose complexity is captured by the Vapnik-Chervonenkis (VC) dimension. The rate-distortion framework, on the other hand, characterizes the average-case performance of a family of data distributions in terms of a quantity called the interpolation dimension, which represents the complexity of the family of data distributions. The resulting bounds do not suffer from the pessimism typical of the PAC framework, particularly when the training set is small.

We propose two low-complexity lattice code constructions that have competitive coding and shaping gains. The first construction, named systematic Voronoi shaping, maps short blocks of integers to the dithered Voronoi integers, which are dithered integers that are uniformly distributed over the Voronoi region of a low-dimensional shaping lattice. Then, these dithered Voronoi integers are encoded using a high-dimensional lattice retaining the same shaping and coding gains of lowand high-dimensional lattices. A drawback to this construction is that there is no isomorphism between the underlying message and the lattice code, preventing its use in applications such as compute-and-forward. Therefore, we propose a second construction, called mixed nested lattice codes, in which a high-dimensional coding lattice is nested inside a concatenation of low-dimensional shaping lattices. This construction not only retains the same shaping/coding gains as first construction but also provides the desired algebraic structure. We numerically study these methods, for point-to-point channels as well as compute-and-forward using low-density lattice codes as coding lattices and E8 and Barnes-Wall as shaping lattices. Numerical results indicate a shaping gain of up to 0.86 dB, compared with the state-ofthe-art of 0.4 dB; furthermore, the proposed method has lower complexity than the state-of-the-art approaches.

We propose a class of signaling schemes that leverage transmitter cooperation in wireless networks employing compute-and-forward or physical-layer network coding. We devise a lattice-coding approach to superposition block Markov encoding from which we construct a cooperative lattice coding strategy. Transmitters broadcast lattice codewords, decode each other's messages, and then cooperatively transmit resolution information which aids relays in decoding finite-field linear combinations of the incoming messages. We show that cooperation provides a substantial improvement in achievable computation rate and outage probability over noncooperative strategies. Using this strategy, we derive a new achievability scheme for the multiway relay channel, the rates of which are near capacity in many regimes and enjoy a diversity advantage over noncooperation.

In this paper, a multiscale approach to spectrum sensing in cognitive cellular networks is analyzed. Observing that wireless interference decays with distance, and that estimating the entire spectrum occupancy across the network entails substantial energy cost and communication overhead, a protocol for distributed spectrum estimation is defined by which secondary users maintain fine-grained estimates of the spectrum occupancy of nearby cells, but coarse-grained estimates of that of distant cells. This is accomplished by arranging the cellular network into a hierarchy of increasingly coarser macro-cells and having secondary users fuse local spectrum estimates up the hierarchy. The spectrum occupancy is modeled as a Markov process, and the system is optimized by defining a probabilistic framework for spectrum sensing and information exchange that balances improvements in spectrum estimation against energy costs. The performance of the multiscale scheme is evaluated numerically, showing that it offers substantial improvements in energy efficiency over local estimation. On the other hand, it is shown that schemes that attempt to estimate the state of the whole network perform poorly, due to the excessive cost of performing information exchange with far away cells, and to the fact that, knowing the spectrum occupancy of distant cells, which experience low interference levels, results in a small increase in reward.

We derive fundamental limits on the reliable classification of linear and affine subspaces from noisy, linear features. Drawing an analogy between discrimination among subspaces and communication over vector wireless channels, we define two Shannon-inspired characterizations of asymptotic classifier performance. First, we define the classification capacity, which characterizes the necessary and sufficient conditions for vanishing misclassification probability as the signal dimension, the number of features, and the number of subspaces to be discriminated all approach infinity. Second, we define the diversity-discrimination tradeoff, which, by analogy with the diversity-multiplexing tradeoff of fading vector channels, characterizes relationships between the number of discernible subspaces and the misclassification probability as the feature noise power approaches zero. We derive upper and lower bounds on these quantities which are tight in many regimes. Numerical results, including a face recognition application, validate the results in practice.

We propose a class of practical efficient lattice codes for real-valued full-duplex one- and two-way relay channels. First, we investigate the problem from a theoretical perspective, proposing lattice-coding instantiations of superposition block Markov encoding. Our encoding/decoding strategies recover the well-known decode-and-foward rates for the one-way relay channel and a previously-proven rate region for the two-way relay channel. Then, we construct practical, low-complexity implementations of these schemes using low-density lattice codes. Simulations show that our schemes achieve performance as close as 2.5 dB away from theoretical limits. Finally, we show that, due to features inherent to full-duplex relaying and practical codes, the gap to theoretical limits depends on the channel gains and transmit power of the relay relative to the source(s). We characterize this gap analytically, providing insight into the design of practical full-duplex relay systems.

Using Shannon theory, we derive fundamental, asymptotic limits on the classification of low-dimensional subspaces from compressive measurements. We identify a syntactic equivalence between the classification of subspaces and the communication of codewords over non-coherent, multiple-antenna channels, from which we derive sharp bounds on the number of classes that can be discriminated with low misclassification probability as a function of the signal dimensionality and the signal-to-noise ratio. While the bounds are asymptotic in the limit of high dimension, they provide intuition for classifier design at finite dimension. We validate this intuition via an application to face recognition.

Repurposing tools and intuitions from Shannon theory, we derive fundamental limits on the reliable classification of high-dimensional signals from low-dimensional features. We focus on the classification of linear and affine subspaces and suppose the features to be noisy linear projections. Leveraging a syntactic equivalence of discrimination between subspaces and communications over vector wireless channels, we derive asymptotic bounds on classifier performance. First, we define the classification capacity, which characterizes necessary and sufficient relationships between the signal dimension, the number of features, and the number of classes to be discriminated, as all three quantities approach infinity. Second, we define the diversitydiscrimination tradeoff, which characterizes relationships between the number of classes and the misclassification probability as the signal-to-noise ratio approaches infinity. We derive inner and outer bounds on these measures, revealing precise relationships between signal dimension and classifier performance.

We study practical, efficient codes for the Gaussian relay channel. It has been demonstrated that low-density lattice codes (LDLCs) can provide near-capacity performance for point-to-point Gaussian channels. We present an LDLC formulation that provides performance near the decode-and-forward inner bound of the relay channel capacity. We employ a superposition block Markov strategy tailored to LDLCs and design an appropriate iterative decoder. We characterize the error performance via simulations, showing that our scheme achieves performance only 2dB away from the decode-and-forward bound.

We study layered wireless networks in which destinations decode linear combinations of transmitted messages over a finite field. We propose amplify-and-compute, a simple but effective scheme in which sources encode their messages with lattice codes, relays employ amplify-and-forward relaying, and destinations decode incoming signals to integer combinations of lattice codewords. We focus on the two-user setting and show that, by carefully choosing relay amplification weights, it is possible to align the equivalent end-to-end channel to an arbitrary matrix of non-zero integers (up to a set of channel matrices of zero measure). Such a choice achieves a computation rate to within a gap to capacity that is independent of the SNR. Amplify-and-compute therefore achieves the maximum degrees of freedom while providing good performance at moderate SNR. Finally, we show that amplify-and-compute offers similar performance when applied to layered two-user interference networks.

Motivated by applications in high-dimensional signal processing, we derive fundamental limits on the performance of compressive linear classifiers. By analogy with Shannon theory, we define the classification capacity, which quantifies the maximum number of classes that can be discriminated with low probability of error, and the diversity-discrimination tradeoff, which quantifies the tradeoff between the number of classes and the probability of classification error. For classification of Gaussian mixture models, we identify a duality between classification and communications over non-coherent multiple-antenna channels. This duality allows us to characterize the classification capacity and diversity-discrimination tradeoff using existing results from multiple-antenna communication. We also identify the easiest possible classification problems, which correspond to low-dimensional subspaces drawn from an appropriate Grassmann manifold.

We introduce an approach to gossip algorithms that exploits three aspects of the wireless medium: superposition, broadcast, and power control. Instead of sending pairwise messages between neighbors on a fixed network topology, we construct gossip algorithms in which nodes can simultaneously recover multiple neighbors' messages and in which nodes can adjust the set of their neighbors by adjusting transmit power. We present two averaging algorithms, each based on a hierarchical clustering of the network. In the first algorithm, clusters of nodes transmit their estimates locally and randomly select a representative node for communications at the next level. In the second, each cluster mutually averages and then cooperatively transmits at the next level. For path-loss environments, these schemes achieve order-optimal or near order-optimal performance.

It has been conjectured that lattice codes are good for (almost) everything. As an additional bit of evidence for this claim, we offer a few results showing the utility of lattice codes for the AWGN relay channel. We show that the decode-and-forward rates of the relay channel can be achieved using lattice encoding and decoding. We present an encoding/decoding technique that uses a doubly-nested lattice code. Encoding is accomplished using a combination of superposition encoding and block Markov encoding, while decoding is accomplished using a strategy reminiscent of Cover and El Gamal's list decoding. Our technique can be extended to a wide variety of relay topologies, including the half-duplex relay channel and the cooperative multiple-access channel.

We study user cooperation in the context of physical-layer network coding. We examine a system in which users cooperatively transmit their messages to receivers whose task is to recover a finite-field linear combination of the users' messages. We present a cooperative scheme, based on a lattice-coding approach to block Markov encoding, that improves the computation rate over that of existing non-cooperative techniques. We apply our results to a simple relay network, showing that when inter-user gains are relatively strong, cooperative computation significantly improves network throughput.

Motivated by recent work applying lattice codes to physical-layer network coding, we study a system in which the receiver computes a finite-field linear combination of users' messages. Previous lattice techniques require that the linear combination be closely matched to the channel coefficients in order to achieve a non-trivial computation rate. To overcome this issue, we present a cooperative computation scheme based on a lattice-coding approach to block Markov encoding. In addition to improving the computation rate, the cooperative approach significantly increases the set of linear combinations that can be recovered at the receiver, increasing the flexibility of wireless network-coded systems.

User cooperation improves performance in wireless systems, but it requires other users to expend energy acting as relays. When energy is scarce, users have incentive to refuse to cooperate in order to conserve resources. Therefore, we investigate cooperative communications from an energy- efficiency perspective. We present a cellular framework in which two mobile users, who desire to communicate with a common base station, may cooperate via decode-and-forward relaying. We maximize users' bits-per-energy efficiency by defining the achievable bits-per-energy region and finding the power allocations that achieve its Pareto boundary. To find an efficient approach that gives selfish users incentive to cooperate, we apply game theory, finding the power allocations that achieve the Nash bargaining solution. Numerical results indicate that the Nash bargain provides a fair and efficient compromise and that both users obtain noticeably improved bits-per-energy efficiency via cooperation.

Satisficing game theory offers an alternative to classical game theory that describes a flexible model of players' social interactions. Players' utility functions depend on other players' attitudes rather than simply their actions. However, satisficing players with conflicting attitudes may enact dysfunctional behaviors, which results in poor performance. We present an evolutionary method by which a population of players may adapt their attitudes to improve payoff. In addition, we extend the Nash-equilibrium concept to satisficing games, showing that the method leads players toward the equilibrium in their attitudes. We apply these ideas to the stag hunt--a simple game in which cooperation does not easily evolve from noncooperation. The evolutionary method provides two major contributions. First, satisficing players may improve their performance by adapting their attitudes. Second, numerical results demonstrate that cooperation in the stag hunt can emerge much more readily under the method we present than under traditional evolutionary models.

We investigate the use of multi-user detection to improve performance in MIMO interference networks. Unfortunately, while multi-user detection often allows higher data rates, it greatly complicates the problem: in addition to choosing a transmit covariance for each transmitter, we must decide which signals each receiver will detect and which data rates make such detection feasible. We discuss methods to optimize the data rates in two ways: maximizing the sum throughput of the network, and choosing rates based on the Kalai-Smorodinsky bargaining solution from cooperative game theory. Simulation results suggest that, while sum-rate maximization yields higher average throughput, the Kalai-Smorodinsky solution provides a superior solution in terms of fairness. The simulations also suggest that multi-user detection significantly improves network performance.

We examine signaling strategies for wireless MIMO networks with interference. Previous approaches have focused on maximizing either individual or total throughput, resulting in an inefficient or potentially unfair allocation of resources. We propose two methods motivated by game-theoretic results. First, we extend the non-cooperative Nash equilibrium proposed in previous literature. Second, we present a cooperative method based on the Nash bargaining solution which provides an axiomatic arbitration scheme. Simulation results show that the Nash bargaining solution provides a fair allocation of resources without significantly sacrificing total throughput.

A potentially useful model for multi-agent system design is the Stag Hunt game. However, when viewed in the context of classical game theory, this game cannot readily evolve a non-cooperative society into a cooperative one. Satisficing game theory provides a natural framework within which it is possible for players to possess more flexibility with regard to their choices than conventional theory affords, thereby making it possible for cooperation to emerge via replicator dynamics in the Stag Hunt.

Searching a random graph is known to be computationally complex. The classic example for the single agent case is the traveling salesman problem. In this paper, we generalize to the multi-agent case where n autonomous agents must cooperate to visit all the nodes of a random graph in an efficient manner. We impose a limitation on the agent's ability to communicate with each other. A satisficing game approach is ideally suited to this problem since it accommodates multiple solutions for each player and provides the opportunity for negotiation. We demonstrate performance of this approach on both deterministic and random graphs with up to 100 nodes.