Probabilistic inference in high-dimensional state-space models is computationally challenging. For many spatiotemporal systems, however, prior knowledge about the dependency structure of state variables is available. We leverage this structure to develop a computationally efficient approach to state estimation and learning in graph-structured state-space models with (partially) unknown dynamics and limited historical data. Building on recent methods that combine ideas from deep learning with principled inference in Gaussian Markov random fields (GMRF), we reformulate graph-structured state-space models as Deep GMRFs defined by simple spatial and temporal graph layers. This results in a flexible spatiotemporal prior that can be learned efficiently from a single time sequence via variational inference. Under linear Gaussian assumptions, we retain a closed-form posterior, which can be sampled efficiently using the conjugate gradient method, scaling favourably compared to classical Kalman filter based approaches
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This paper studies the design and analysis of approximation algorithms for aggregating preferences over combinatorial domains, represented using Conditional Preference Networks (CP-nets). Its focus is on aggregating preferences over so-called \emph{swaps}, for which optimal solutions in general are already known to be of exponential size. We first analyze a trivial 2-approximation algorithm that simply outputs the best of the given input preferences, and establish a structural condition under which the approximation ratio of this algorithm is improved to $4/3$. We then propose a polynomial-time approximation algorithm whose outputs are provably no worse than those of the trivial algorithm, but often substantially better. A family of problem instances is presented for which our improved algorithm produces optimal solutions, while, for any $\varepsilon$, the trivial algorithm can\emph{not}\/ attain a $(2-\varepsilon)$-approximation. These results may lead to the first polynomial-time approximation algorithm that solves the CP-net aggregation problem for swaps with an approximation ratio substantially better than $2$.
Many neural network architectures have been shown to be Turing Complete, and can thus implement arbitrary algorithms. However, Transformers are unique in that they can implement gradient-based learning algorithms \emph{under simple parameter configurations}. A line of recent work shows that linear Transformers naturally learn to implement gradient descent (GD) when trained on a linear regression in-context learning task. But the linearity assumption (either in the Transformer architecture or in the learning task) is far from realistic settings where non-linear activations crucially enable Transformers to learn complicated non-linear functions. In this paper, we provide theoretical and empirical evidence that non-linear Transformers can, and \emph{in fact do}, learn to implement learning algorithms to learn non-linear functions in context. Our results apply to a broad class of combinations of non-linear architectures, and non-linear in-context learning tasks. Interestingly, we show that the optimal choice of non-linear activation depends in a natural way on the non-linearity of the learning task.
Bilevel optimization has received more and more attention recently due to its wide applications in machine learning. In this paper, we consider bilevel optimization in decentralized networks. In particular, we propose a novel single-loop algorithm for solving decentralized bilevel optimization with strongly convex lower level problem. Our algorithm is fully single-loop and does not require heavy matrix-vector multiplications when approximating the hypergradient. Moreover, unlike existing methods for decentralized bilevel optimization and federated bilevel optimization, our algorithm does not require any gradient heterogeneity assumption. Our analysis shows that the proposed algorithm achieves a sublinear convergence rate. Experimental results on hyperparameter optimization problem with both synthetic and MNIST data sets demonstrate the efficiency of the proposed algorithm.
In critical machine learning applications, ensuring fairness is essential to avoid perpetuating social inequities. In this work, we address the challenges of reducing bias and improving accuracy in data-scarce environments, where the cost of collecting labeled data prohibits the use of large, labeled datasets. In such settings, active learning promises to maximize marginal accuracy gains of small amounts of labeled data. However, existing applications of active learning for fairness fail to deliver on this, typically requiring large labeled datasets, or failing to ensure the desired fairness tolerance is met on the population distribution. To address such limitations, we introduce an innovative active learning framework that combines an exploration procedure inspired by posterior sampling with a fair classification subroutine. We demonstrate that this framework performs effectively in very data-scarce regimes, maximizing accuracy while satisfying fairness constraints with high probability. We evaluate our proposed approach using well-established real-world benchmark datasets and compare it against state-of-the-art methods, demonstrating its effectiveness in producing fair models, and improvement over existing methods.
Energy-based models (EBMs) are generative models inspired by statistical physics with a wide range of applications in unsupervised learning. Their performance is best measured by the cross-entropy (CE) of the model distribution relative to the data distribution. Using the CE as the objective for training is however challenging because the computation of its gradient with respect to the model parameters requires sampling the model distribution. Here we show how results for nonequilibrium thermodynamics based on Jarzynski equality together with tools from sequential Monte-Carlo sampling can be used to perform this computation efficiently and avoid the uncontrolled approximations made using the standard contrastive divergence algorithm. Specifically, we introduce a modification of the unadjusted Langevin algorithm (ULA) in which each walker acquires a weight that enables the estimation of the gradient of the cross-entropy at any step during GD, thereby bypassing sampling biases induced by slow mixing of ULA. We illustrate these results with numerical experiments on Gaussian mixture distributions as well as the MNIST dataset. We show that the proposed approach outperforms methods based on the contrastive divergence algorithm in all the considered situations.
Deep neural networks (DNNs) have succeeded in many different perception tasks, e.g., computer vision, natural language processing, reinforcement learning, etc. The high-performed DNNs heavily rely on intensive resource consumption. For example, training a DNN requires high dynamic memory, a large-scale dataset, and a large number of computations (a long training time); even inference with a DNN also demands a large amount of static storage, computations (a long inference time), and energy. Therefore, state-of-the-art DNNs are often deployed on a cloud server with a large number of super-computers, a high-bandwidth communication bus, a shared storage infrastructure, and a high power supplement. Recently, some new emerging intelligent applications, e.g., AR/VR, mobile assistants, Internet of Things, require us to deploy DNNs on resource-constrained edge devices. Compare to a cloud server, edge devices often have a rather small amount of resources. To deploy DNNs on edge devices, we need to reduce the size of DNNs, i.e., we target a better trade-off between resource consumption and model accuracy. In this dissertation, we studied four edge intelligence scenarios, i.e., Inference on Edge Devices, Adaptation on Edge Devices, Learning on Edge Devices, and Edge-Server Systems, and developed different methodologies to enable deep learning in each scenario. Since current DNNs are often over-parameterized, our goal is to find and reduce the redundancy of the DNNs in each scenario.
We describe ACE0, a lightweight platform for evaluating the suitability and viability of AI methods for behaviour discovery in multiagent simulations. Specifically, ACE0 was designed to explore AI methods for multi-agent simulations used in operations research studies related to new technologies such as autonomous aircraft. Simulation environments used in production are often high-fidelity, complex, require significant domain knowledge and as a result have high R&D costs. Minimal and lightweight simulation environments can help researchers and engineers evaluate the viability of new AI technologies for behaviour discovery in a more agile and potentially cost effective manner. In this paper we describe the motivation for the development of ACE0.We provide a technical overview of the system architecture, describe a case study of behaviour discovery in the aerospace domain, and provide a qualitative evaluation of the system. The evaluation includes a brief description of collaborative research projects with academic partners, exploring different AI behaviour discovery methods.
Federated Learning (FL) is a decentralized machine-learning paradigm, in which a global server iteratively averages the model parameters of local users without accessing their data. User heterogeneity has imposed significant challenges to FL, which can incur drifted global models that are slow to converge. Knowledge Distillation has recently emerged to tackle this issue, by refining the server model using aggregated knowledge from heterogeneous users, other than directly averaging their model parameters. This approach, however, depends on a proxy dataset, making it impractical unless such a prerequisite is satisfied. Moreover, the ensemble knowledge is not fully utilized to guide local model learning, which may in turn affect the quality of the aggregated model. Inspired by the prior art, we propose a data-free knowledge distillation} approach to address heterogeneous FL, where the server learns a lightweight generator to ensemble user information in a data-free manner, which is then broadcasted to users, regulating local training using the learned knowledge as an inductive bias. Empirical studies powered by theoretical implications show that, our approach facilitates FL with better generalization performance using fewer communication rounds, compared with the state-of-the-art.
Knowledge graph embedding, which aims to represent entities and relations as low dimensional vectors (or matrices, tensors, etc.), has been shown to be a powerful technique for predicting missing links in knowledge graphs. Existing knowledge graph embedding models mainly focus on modeling relation patterns such as symmetry/antisymmetry, inversion, and composition. However, many existing approaches fail to model semantic hierarchies, which are common in real-world applications. To address this challenge, we propose a novel knowledge graph embedding model---namely, Hierarchy-Aware Knowledge Graph Embedding (HAKE)---which maps entities into the polar coordinate system. HAKE is inspired by the fact that concentric circles in the polar coordinate system can naturally reflect the hierarchy. Specifically, the radial coordinate aims to model entities at different levels of the hierarchy, and entities with smaller radii are expected to be at higher levels; the angular coordinate aims to distinguish entities at the same level of the hierarchy, and these entities are expected to have roughly the same radii but different angles. Experiments demonstrate that HAKE can effectively model the semantic hierarchies in knowledge graphs, and significantly outperforms existing state-of-the-art methods on benchmark datasets for the link prediction task.
The potential of graph convolutional neural networks for the task of zero-shot learning has been demonstrated recently. These models are highly sample efficient as related concepts in the graph structure share statistical strength allowing generalization to new classes when faced with a lack of data. However, knowledge from distant nodes can get diluted when propagating through intermediate nodes, because current approaches to zero-shot learning use graph propagation schemes that perform Laplacian smoothing at each layer. We show that extensive smoothing does not help the task of regressing classifier weights in zero-shot learning. In order to still incorporate information from distant nodes and utilize the graph structure, we propose an Attentive Dense Graph Propagation Module (ADGPM). ADGPM allows us to exploit the hierarchical graph structure of the knowledge graph through additional connections. These connections are added based on a node's relationship to its ancestors and descendants and an attention scheme is further used to weigh their contribution depending on the distance to the node. Finally, we illustrate that finetuning of the feature representation after training the ADGPM leads to considerable improvements. Our method achieves competitive results, outperforming previous zero-shot learning approaches.
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