We consider Ising models on the hypercube with a general interaction matrix $J$, and give a polynomial time sampling algorithm when all but $O(1)$ eigenvalues of $J$ lie in an interval of length one, a situation which occurs in many models of interest. This was previously known for the Glauber dynamics when *all* eigenvalues fit in an interval of length one; however, a single outlier can force the Glauber dynamics to mix torpidly. Our general result implies the first polynomial time sampling algorithms for low-rank Ising models such as Hopfield networks with a fixed number of patterns and Bayesian clustering models with low-dimensional contexts, and greatly improves the polynomial time sampling regime for the antiferromagnetic/ferromagnetic Ising model with inconsistent field on expander graphs. It also improves on previous approximation algorithm results based on the naive mean-field approximation in variational methods and statistical physics. Our approach is based on a new fusion of ideas from the MCMC and variational inference worlds. As part of our algorithm, we define a new nonconvex variational problem which allows us to sample from an exponential reweighting of a distribution by a negative definite quadratic form, and show how to make this procedure provably efficient using stochastic gradient descent. On top of this, we construct a new simulated tempering chain (on an extended state space arising from the Hubbard-Stratonovich transform) which overcomes the obstacle posed by large positive eigenvalues, and combine it with the SGD-based sampler to solve the full problem.
This paper leverages recent developments in reinforcement learning and deep learning to solve the supply chain inventory management problem, a complex sequential decision-making problem consisting of determining the optimal quantity of products to produce and ship to different warehouses over a given time horizon. A mathematical formulation of the stochastic two-echelon supply chain environment is given, which allows an arbitrary number of warehouses and product types to be managed. Additionally, an open-source library that interfaces with deep reinforcement learning algorithms is developed and made publicly available for solving the inventory management problem. Performances achieved by state-of-the-art deep reinforcement learning algorithms are compared through a rich set of numerical experiments on synthetically generated data. The experimental plan is designed and performed, including different structures, topologies, demands, capacities, and costs of the supply chain. Results show that the PPO algorithm adapts very well to different characteristics of the environment. The VPG algorithm almost always converges to a local maximum, even if it typically achieves an acceptable performance level. Finally, A3C is the fastest algorithm, but just like the VPG, it never achieves the best performance when compared to PPO. In conclusion, numerical experiments show that deep reinforcement learning performs consistently better than standard inventory management strategies, such as the static (s, Q)-policy. Thus, it can be considered a practical and effective option for solving real-world instances of the stochastic two-echelon supply chain problem.
We define a notion of "non-backtracking" matrix associated to any symmetric matrix, and we prove a "Ihara-Bass" type formula for it. Previously, these notions were known only for symmetric 0/1 matrices. We use this theory to prove new results on polynomial-time strong refutations of random constraint satisfaction problems with $k$ variables per constraints (k-CSPs). For a random k-CSP instance constructed out of a constraint that is satisfied by a $p$ fraction of assignments, if the instance contains $n$ variables and $n^{k/2} / \epsilon^2$ constraints, we can efficiently compute a certificate that the optimum satisfies at most a $p+O_k(\epsilon)$ fraction of constraints. Previously, this was known for even $k$, but for odd $k$ one needed $n^{k/2} (\log n)^{O(1)} / \epsilon^2$ random constraints to achieve the same conclusion. Although the improvement is only polylogarithmic, it overcomes a significant barrier to these types of results. Strong refutation results based on current approaches construct a certificate that a certain matrix associated to the k-CSP instance is quasirandom. Such certificate can come from a Feige-Ofek type argument, from an application of Grothendieck's inequality, or from a spectral bound obtained with a trace argument. The first two approaches require a union bound that cannot work when the number of constraints is $o(n^{\lceil k/2 \rceil})$ and the third one cannot work when the number of constraints is $o(n^{k/2} \sqrt{\log n})$.
Named Entity Recognition (NER) is a foundational NLP task that aims to provide class labels like Person, Location, Organisation, Time, and Number to words in free text. Named Entities can also be multi-word expressions where the additional I-O-B annotation information helps label them during the NER annotation process. While English and European languages have considerable annotated data for the NER task, Indian languages lack on that front -- both in terms of quantity and following annotation standards. This paper releases a significantly sized standard-abiding Hindi NER dataset containing 109,146 sentences and 2,220,856 tokens, annotated with 11 tags. We discuss the dataset statistics in all their essential detail and provide an in-depth analysis of the NER tag-set used with our data. The statistics of tag-set in our dataset show a healthy per-tag distribution, especially for prominent classes like Person, Location and Organisation. Since the proof of resource-effectiveness is in building models with the resource and testing the model on benchmark data and against the leader-board entries in shared tasks, we do the same with the aforesaid data. We use different language models to perform the sequence labelling task for NER and show the efficacy of our data by performing a comparative evaluation with models trained on another dataset available for the Hindi NER task. Our dataset helps achieve a weighted F1 score of 88.78 with all the tags and 92.22 when we collapse the tag-set, as discussed in the paper. To the best of our knowledge, no available dataset meets the standards of volume (amount) and variability (diversity), as far as Hindi NER is concerned. We fill this gap through this work, which we hope will significantly help NLP for Hindi. We release this dataset with our code and models at https://github.com/cfiltnlp/HiNER
We study learning contextual MDPs using a function approximation for both the rewards and the dynamics. We consider both the case where the dynamics is known and unknown, and the case that the dynamics dependent or independent of the context. For all four models we derive polynomial sample and time complexity (assuming an efficient ERM oracle). Our methodology gives a general reduction from learning contextual MDP to supervised learning.
In time-division duplexing (TDD) millimeter-wave (mmWave) massive multiple-input multiple-output (MIMO) systems, the reciprocity mismatch severely degrades the performance of the hybrid beamforming (HBF). In this work, to mitigate the detrimental effect of the reciprocity mismatch, we investigate reciprocity calibration for the mmWave-HBF system with a fully-connected phase shifter network. To reduce the overhead and computational complexity of reciprocity calibration, we first decouple digital radio frequency (RF) chains and analog RF chains with beamforming design. Then, the entire calibration problem of the HBF system is equivalently decomposed into two subproblems corresponding to the digital-chain calibration and analog-chain calibration. To solve the calibration problems efficiently, a closed-form solution to the digital-chain calibration problem is derived, while an iterative-alternating optimization algorithm for the analog-chain calibration problem is proposed. To measure the performance of the proposed algorithm, we derive the Cram\'er-Rao lower bound on the errors in estimating mismatch coefficients. The results reveal that the estimation errors of mismatch coefficients of digital and analog chains are uncorrelated, and that the mismatch coefficients of receive digital chains can be estimated perfectly. Simulation results are presented to validate the analytical results and to show the performance of the proposed calibration approach.
Visual (image, video) quality assessments can be modelled by visual features in different domains, e.g., spatial, frequency, and temporal domains. Perceptual mechanisms in the human visual system (HVS) play a crucial role in generation of quality perception. This paper proposes a general framework for no-reference visual quality assessment using efficient windowed transformer architectures. A lightweight module for multi-stage channel attention is integrated into Swin (shifted window) Transformer. Such module can represent appropriate perceptual mechanisms in image quality assessment (IQA) to build an accurate IQA model. Meanwhile, representative features for image quality perception in the spatial and frequency domains can also be derived from the IQA model, which are then fed into another windowed transformer architecture for video quality assessment (VQA). The VQA model efficiently reuses attention information across local windows to tackle the issue of expensive time and memory complexities of original transformer. Experimental results on both large-scale IQA and VQA databases demonstrate that the proposed quality assessment models outperform other state-of-the-art models by large margins. The complete source code will be published on Github.
A large number of inorganic and organic compounds are able to bind DNA and form complexes, among which drug-related molecules are important. Chromatin accessibility changes not only directly affects drug-DNA interactions, but also promote or inhibit the expression of critical genes associated with drug resistance by affecting the DNA binding capacity of TFs and transcriptional regulators. However, Biological experimental techniques for measuring it are expensive and time consuming. In recent years, several kinds of computational methods have been proposed to identify accessible regions of the genome. Existing computational models mostly ignore the contextual information of bases in gene sequences. To address these issues, we proposed a new solution named SemanticCAP. It introduces a gene language model which models the context of gene sequences, thus being able to provide an effective representation of a certain site in gene sequences. Basically, we merge the features provided by the gene language model into our chromatin accessibility model. During the process, we designed some methods to make feature fusion smoother. Compared with other systems under public benchmarks, our model proved to have better performance.
Gaussian Process (GP) formulation of continuoustime trajectory offers a fast solution to the motion planning problem via probabilistic inference on factor graph. However, often the solution converges to in-feasible local minima and the planned trajectory is not collision-free. We propose a message passing algorithm that is more sensitive to obstacles with fast convergence time. We leverage the utility of min-sum message passing algorithm that performs local computations at each node to solve the inference problem on factor graph. We first introduce the notion of compound factor node to transform the factor graph to a linearly structured graph. We next develop an algorithm denoted as Min-sum Message Passing algorithm for Motion Planning (MS2MP) that combines numerical optimization with message passing to find collision-free trajectories. MS2MP performs numerical optimization to solve non-linear least square minimization problem at each compound factor node and then exploits the linear structure of factor graph to compute the maximum a posteriori (MAP) estimation of complete graph by passing messages among graph nodes. The decentralized optimization approach of each compound node increases sensitivity towards avoiding obstacles for harder planning problems. We evaluate our algorithm by performing extensive experiments for exemplary motion planning tasks for a robot manipulator. Our evaluation reveals that MS2MP improves existing work in convergence time and success rate.
There has been a growing interest in the evolutionary computation community to compute a diverse set of high-quality solutions for a given optimisation problem. This can provide the practitioners with invaluable information about the solution space and robustness against imperfect modelling and minor problems' changes. It also enables the decision-makers to involve their interests and choose between various solutions. In this study, we investigate for the first time a prominent multi-component optimisation problem, namely the Traveling Thief Problem (TTP), in the context of evolutionary diversity optimisation. We introduce a bi-level evolutionary algorithm to maximise the structural diversity of the set of solutions. Moreover, we examine the inter-dependency among the components of the problem in terms of structural diversity and empirically determine the best method to obtain diversity. We also conduct a comprehensive experimental investigation to examine the introduced algorithm and compare the results to another recently introduced framework based on the use of Quality Diversity (QD). Our experimental results show a significant improvement of the QD approach in terms of structural diversity for most TTP benchmark instances.