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In time-series analysis, many recent works seek to provide a unified view and representation for time-series across multiple domains, leading to the development of foundation models for time-series data. Despite diverse modeling techniques, existing models are black boxes and fail to provide insights and explanations about their representations. In this paper, we present VQShape, a pre-trained, generalizable, and interpretable model for time-series representation learning and classification. By introducing a novel representation for time-series data, we forge a connection between the latent space of VQShape and shape-level features. Using vector quantization, we show that time-series from different domains can be described using a unified set of low-dimensional codes, where each code can be represented as an abstracted shape in the time domain. On classification tasks, we show that the representations of VQShape can be utilized to build interpretable classifiers, achieving comparable performance to specialist models. Additionally, in zero-shot learning, VQShape and its codebook can generalize to previously unseen datasets and domains that are not included in the pre-training process. The code and pre-trained weights are available at https://github.com/YunshiWen/VQShape., Comment: Accepted by Neural Information Processing Systems (NeurIPS) 2024

This paper aims at developing novel shuffling gradient-based methods for tackling two classes of minimax problems: nonconvex-linear and nonconvex-strongly concave settings. The first algorithm addresses the nonconvex-linear minimax model and achieves the state-of-the-art oracle complexity typically observed in nonconvex optimization. It also employs a new shuffling estimator for the "hyper-gradient", departing from standard shuffling techniques in optimization. The second method consists of two variants: semi-shuffling and full-shuffling schemes. These variants tackle the nonconvex-strongly concave minimax setting. We establish their oracle complexity bounds under standard assumptions, which, to our best knowledge, are the best-known for this specific setting. Numerical examples demonstrate the performance of our algorithms and compare them with two other methods. Our results show that the new methods achieve comparable performance with SGD, supporting the potential of incorporating shuffling strategies into minimax algorithms., Comment: 45 pages, 5 figures (38th Conference on Neural Information Processing Systems (NeurIPS 2024))

Radio pulsars allow the study of the ionised interstellar medium and its dispersive effects, a major noise source in gravitational wave searches using pulsars. In this paper, we compare the functionality and reliability of three commonly used schemes to measure temporal variations in interstellar propagation effects in pulsar-timing data. We carry out extensive simulations at low observing frequencies (100-200 MHz) by injecting long-term correlated noise processes with power-law spectra and white noise, to evaluate the robustness, accuracy and precision of the following three mitigation methods: epoch-wise (EW) measurements of interstellar dispersion; the DMX method of simultaneous, piece-wise fits to interstellar dispersion; and DMGP, which models dispersion variations through Gaussian processes using a Bayesian analysis method. We then evaluate how reliably the input signals are reconstructed and how the various methods react to the presence of achromatic long-period noise. All the methods perform well, provided the achromatic long-period noise is modeled for DMX and DMGP. The most precise method is DMGP, followed by DMX and EW, while the most accurate is EW, followed by DMX and DMGP. We also test different scenarios including simulations of L-band ToAs and realistic DM injection, with no significant variation in the obtained results. Given the nature of our simulations and our scope, we deem that EW is the most reliable method to study the Galactic ionized media. Future works should be conducted to confirm this result via more realistic simulations. We note that DM GP and DMX seem to be the most performing techniques in removing long-term correlated noise, and hence for gravitational wave studies. However, full simulations of pulsar timing array experiments are needed to support this interpretation.

Physics-informed neural networks (PINNs) incorporate physical laws into their training to efficiently solve partial differential equations (PDEs) with minimal data. However, PINNs fail to guarantee adherence to conservation laws, which are also important to consider in modeling physical systems. To address this, we proposed PINN-Proj, a PINN-based model that uses a novel projection method to enforce conservation laws. We found that PINN-Proj substantially outperformed PINN in conserving momentum and lowered prediction error by three to four orders of magnitude from the best benchmark tested. PINN-Proj also performed marginally better in the separate task of state prediction on three PDE datasets., Comment: Accepted to NeurIPS 2024 Workshop on Data-driven and Differentiable Simulations, Surrogates, and Solvers

Context. The spectra of fast-rotating A-type stars have strongly broadened absorption lines. This effect causes blending of the absorption lines, hindering the measurement of the abundances of the elements that are in the stellar photosphere. Aims. As the exoplanet transits across its host star, it obscures the stellar spectrum that is emitted from directly behind the planet. We aim to extract this obscured spectrum because it is less affected by rotational broadening, resolving the blending of weak lines of elements that would otherwise remain inaccessible. This allows us to more precisely measure the metal abundances in ultra-hot Jupiter systems, many of which have fast rotating host stars. Methods. We develop a novel method that isolates the stellar spectra behind the planet during a spectral time-series, and reconstructs the disc-integrated non-broadened spectrum of the host star. We have systematically tested this method with model-generated spectra of the transit of WASP-189 b across its fast-rotating A-type host star, assessing the effects of limb darkening, choice of absorption lines, signal to noise regime; and demonstrating the sensitivity to photospheric parameters ($T_{\text{eff}}$, $\log g$) and elemental abundances. We apply the method to observations by the HARPS high-resolution spectrograph. Results. For WASP-189, we obtain the metallicity and photospheric abundances for several species previously not reported in literature, Mg, Ca and Ti, with significantly improved accuracy compared to the ordinary broadened stellar spectrum. This method can be generally applied to other transiting systems in which abundance determinations via spectral synthesis are imprecise due to severe line blending. It is important to accurately determine the photospheric properties of exoplanet host stars, as it can provide further insight into the formation and evolution of the planets., Comment: 13 pages, 6 figures

Foundational models (FMs), pretrained on extensive datasets using self-supervised techniques, are capable of learning generalized patterns from large amounts of data. This reduces the need for extensive labeled datasets for each new task, saving both time and resources by leveraging the broad knowledge base established during pretraining. Most research on FMs has primarily focused on unstructured data, such as text and images, or semi-structured data, like time-series. However, there has been limited attention to structured data, such as tabular data, which, despite its prevalence, remains under-studied due to a lack of clean datasets and insufficient research on the transferability of FMs for various tabular data tasks. In response to this gap, we introduce a framework called TabularFM, which incorporates state-of-the-art methods for developing FMs specifically for tabular data. This includes variations of neural architectures such as GANs, VAEs, and Transformers. We have curated a million of tabular datasets and released cleaned versions to facilitate the development of tabular FMs. We pretrained FMs on this curated data, benchmarked various learning methods on these datasets, and released the pretrained models along with leaderboards for future comparative studies. Our fully open-sourced system provides a comprehensive analysis of the transferability of tabular FMs. By releasing these datasets, pretrained models, and leaderboards, we aim to enhance the validity and usability of tabular FMs in the near future.

The current standard model of cosmology successfully describes a variety of measurements, but the nature of its main ingredients, dark matter and dark energy, remains unknown. Euclid is a medium-class mission in the Cosmic Vision 2015-2025 programme of the European Space Agency (ESA) that will provide high-resolution optical imaging, as well as near-infrared imaging and spectroscopy, over about 14,000 deg^2 of extragalactic sky. In addition to accurate weak lensing and clustering measurements that probe structure formation over half of the age of the Universe, its primary probes for cosmology, these exquisite data will enable a wide range of science. This paper provides a high-level overview of the mission, summarising the survey characteristics, the various data-processing steps, and data products. We also highlight the main science objectives and expected performance., Comment: Accepted for publication in the A&A special issue`Euclid on Sky'

Exoplanets in the ultra-hot Jupiter regime provide an excellent laboratory for testing the impact of stellar irradiation on the dynamics and chemical composition of gas giant atmospheres. In this study, we observed two transits of the ultra-hot Jupiter WASP-189 b with MAROON-X/Gemini-North to probe its high-altitude atmospheric layers, using strong absorption lines. We derived posterior probability distributions for the planetary and stellar parameters by calculating the stellar spectrum behind the planet at every orbital phase during the transit. This was used to correct the Rossiter-McLaughlin imprint on the transmission spectra. Using differential transmission spectroscopy, we detect strong absorption lines of Ca+, Ba+, Na, H$\alpha$, Mg, Fe, and Fe+, providing an unprecedented and detailed view of the atmospheric chemical composition. Ca+ absorption is particularly well suited for analysis through time-resolved narrow-band spectroscopy, owing to its transition lines formed in high-altitude layers. The spectral absorption lines show no significant blueshifts that would indicate high-altitude day-to-night winds, and further analysis is needed to investigate the implications for atmospheric dynamics. These high signal-to-noise observations provide a benchmark data set for testing high-resolution retrievals and the assumptions of atmospheric models. We also simulate observations of WASP-189 b with ANDES/ELT, and show that ANDES will be highly sensitive to the individual absorption lines of a myriad of elements and molecules, including TiO and CO., Comment: 34 pages, 31 figures, accepted for publication in A&A on 16 February 2024

The Stochastic Gradient Descent method (SGD) and its stochastic variants have become methods of choice for solving finite-sum optimization problems arising from machine learning and data science thanks to their ability to handle large-scale applications and big datasets. In the last decades, researchers have made substantial effort to study the theoretical performance of SGD and its shuffling variants. However, only limited work has investigated its shuffling momentum variants, including shuffling heavy-ball momentum schemes for non-convex problems and Nesterov's momentum for convex settings. In this work, we extend the analysis of the shuffling momentum gradient method developed in [Tran et al (2021)] to both finite-sum convex and strongly convex optimization problems. We provide the first analysis of shuffling momentum-based methods for the strongly convex setting, attaining a convergence rate of $O(1/nT^2)$, where $n$ is the number of samples and $T$ is the number of training epochs. Our analysis is a state-of-the-art, matching the best rates of existing shuffling stochastic gradient algorithms in the literature., Comment: Vietnam Journal of Mathematics (VJOM), Special issue dedicated to Dr. Tam\'as Terlaky on the occasion of his 70th birthday, 2024

We develop and analyze stochastic variants of ISTA and a full backtracking FISTA algorithms [Beck and Teboulle, 2009, Scheinberg et al., 2014] for composite optimization without the assumption that stochastic gradient is an unbiased estimator. This work extends analysis of inexact fixed step ISTA/FISTA in [Schmidt et al., 2011] to the case of stochastic gradient estimates and adaptive step-size parameter chosen by backtracking. It also extends the framework for analyzing stochastic line-search method in [Cartis and Scheinberg, 2018] to the proximal gradient framework as well as to the accelerated first order methods.

This paper studies the Partial Optimal Transport (POT) problem between two unbalanced measures with at most $n$ supports and its applications in various AI tasks such as color transfer or domain adaptation. There is hence the need for fast approximations of POT with increasingly large problem sizes in arising applications. We first theoretically and experimentally investigate the infeasibility of the state-of-the-art Sinkhorn algorithm for POT due to its incompatible rounding procedure, which consequently degrades its qualitative performance in real world applications like point-cloud registration. To this end, we propose a novel rounding algorithm for POT, and then provide a feasible Sinkhorn procedure with a revised computation complexity of $\mathcal{\widetilde O}(n^2/\varepsilon^4)$. Our rounding algorithm also permits the development of two first-order methods to approximate the POT problem. The first algorithm, Adaptive Primal-Dual Accelerated Gradient Descent (APDAGD), finds an $\varepsilon$-approximate solution to the POT problem in $\mathcal{\widetilde O}(n^{2.5}/\varepsilon)$, which is better in $\varepsilon$ than revised Sinkhorn. The second method, Dual Extrapolation, achieves the computation complexity of $\mathcal{\widetilde O}(n^2/\varepsilon)$, thereby being the best in the literature. We further demonstrate the flexibility of POT compared to standard OT as well as the practicality of our algorithms on real applications where two marginal distributions are unbalanced., Comment: Accepted to AAAI 2024

Neural networks are powerful tools in various applications, and quantifying their uncertainty is crucial for reliable decision-making. In the deep learning field, the uncertainties are usually categorized into aleatoric (data) and epistemic (model) uncertainty. In this paper, we point out that the existing popular variance attenuation method highly overestimates aleatoric uncertainty. To address this issue, we propose a new estimation method by actively de-noising the observed data. By conducting a broad range of experiments, we demonstrate that our proposed approach provides a much closer approximation to the actual data uncertainty than the standard method.

Foundation models have recently gained attention within the field of machine learning thanks to its efficiency in broad data processing. While researchers had attempted to extend this success to time series models, the main challenge is effectively extracting representations and transferring knowledge from pretraining datasets to the target finetuning dataset. To tackle this issue, we introduce a novel pretraining procedure that leverages supervised contrastive learning to distinguish features within each pretraining dataset. This pretraining phase enables a probabilistic similarity metric, which assesses the likelihood of a univariate sample being closely related to one of the pretraining datasets. Subsequently, using this similarity metric as a guide, we propose a fine-tuning procedure designed to enhance the accurate prediction of the target data by aligning it more closely with the learned dynamics of the pretraining datasets. Our experiments have shown promising results which demonstrate the efficacy of our approach.

Multivariate time series (MTS) analysis prevails in real-world applications such as finance, climate science and healthcare. The various self-attention mechanisms, the backbone of the state-of-the-art Transformer-based models, efficiently discover the temporal dependencies, yet cannot well capture the intricate cross-correlation between different features of MTS data, which inherently stems from complex dynamical systems in practice. To this end, we propose a novel correlated attention mechanism, which not only efficiently captures feature-wise dependencies, but can also be seamlessly integrated within the encoder blocks of existing well-known Transformers to gain efficiency improvement. In particular, correlated attention operates across feature channels to compute cross-covariance matrices between queries and keys with different lag values, and selectively aggregate representations at the sub-series level. This architecture facilitates automated discovery and representation learning of not only instantaneous but also lagged cross-correlations, while inherently capturing time series auto-correlation. When combined with prevalent Transformer baselines, correlated attention mechanism constitutes a better alternative for encoder-only architectures, which are suitable for a wide range of tasks including imputation, anomaly detection and classification. Extensive experiments on the aforementioned tasks consistently underscore the advantages of correlated attention mechanism in enhancing base Transformer models, and demonstrate our state-of-the-art results in imputation, anomaly detection and classification.

Randomized smoothing has recently attracted attentions in the field of adversarial robustness to provide provable robustness guarantees on smoothed neural network classifiers. However, existing works show that vanilla randomized smoothing usually does not provide good robustness performance and often requires (re)training techniques on the base classifier in order to boost the robustness of the resulting smoothed classifier. In this work, we propose two cost-effective approaches to boost the robustness of randomized smoothing while preserving its clean performance. The first approach introduces a new robust training method AdvMacerwhich combines adversarial training and robustness certification maximization for randomized smoothing. We show that AdvMacer can improve the robustness performance of randomized smoothing classifiers compared to SOTA baselines, while being 3x faster to train than MACER baseline. The second approach introduces a post-processing method EsbRS which greatly improves the robustness certificate based on building model ensembles. We explore different aspects of model ensembles that has not been studied by prior works and propose a novel design methodology to further improve robustness of the ensemble based on our theoretical analysis.

The Australian, Chinese, European, Indian, and North American pulsar timing array (PTA) collaborations recently reported, at varying levels, evidence for the presence of a nanohertz gravitational wave background (GWB). Given that each PTA made different choices in modeling their data, we perform a comparison of the GWB and individual pulsar noise parameters across the results reported from the PTAs that constitute the International Pulsar Timing Array (IPTA). We show that despite making different modeling choices, there is no significant difference in the GWB parameters that are measured by the different PTAs, agreeing within $1\sigma$. The pulsar noise parameters are also consistent between different PTAs for the majority of the pulsars included in these analyses. We bridge the differences in modeling choices by adopting a standardized noise model for all pulsars and PTAs, finding that under this model there is a reduction in the tension in the pulsar noise parameters. As part of this reanalysis, we "extended" each PTA's data set by adding extra pulsars that were not timed by that PTA. Under these extensions, we find better constraints on the GWB amplitude and a higher signal-to-noise ratio for the Hellings and Downs correlations. These extensions serve as a prelude to the benefits offered by a full combination of data across all pulsars in the IPTA, i.e., the IPTA's Data Release 3, which will involve not just adding in additional pulsars, but also including data from all three PTAs where any given pulsar is timed by more than as single PTA., Comment: 21 pages, 9 figures, submitted to ApJ

Each round in Differential Private Stochastic Gradient Descent (DPSGD) transmits a sum of clipped gradients obfuscated with Gaussian noise to a central server which uses this to update a global model which often represents a deep neural network. Since the clipped gradients are computed separately, which we call Individual Clipping (IC), deep neural networks like resnet-18 cannot use Batch Normalization Layers (BNL) which is a crucial component in deep neural networks for achieving a high accuracy. To utilize BNL, we introduce Batch Clipping (BC) where, instead of clipping single gradients as in the orginal DPSGD, we average and clip batches of gradients. Moreover, the model entries of different layers have different sensitivities to the added Gaussian noise. Therefore, Adaptive Layerwise Clipping methods (ALC), where each layer has its own adaptively finetuned clipping constant, have been introduced and studied, but so far without rigorous DP proofs. In this paper, we propose {\em a new ALC and provide rigorous DP proofs for both BC and ALC}. Experiments show that our modified DPSGD with BC and ALC for CIFAR-$10$ with resnet-$18$ converges while DPSGD with IC and ALC does not., Comment: 20 pages, 18 Figures

In this work, we investigate the time series representation learning problem using self-supervised techniques. Contrastive learning is well-known in this area as it is a powerful method for extracting information from the series and generating task-appropriate representations. Despite its proficiency in capturing time series characteristics, these techniques often overlook a critical factor - the inherent noise in this type of data, a consideration usually emphasized in general time series analysis. Moreover, there is a notable absence of attention to developing efficient yet lightweight encoder architectures, with an undue focus on delivering contrastive losses. Our work address these gaps by proposing an innovative training strategy that promotes consistent representation learning, accounting for the presence of noise-prone signals in natural time series. Furthermore, we propose an encoder architecture that incorporates dilated convolution within the Inception block, resulting in a scalable and robust network with a wide receptive field. Experimental findings underscore the effectiveness of our method, consistently outperforming state-of-the-art approaches across various tasks, including forecasting, classification, and abnormality detection. Notably, our method attains the top rank in over two-thirds of the classification UCR datasets, utilizing only 40% of the parameters compared to the second-best approach. Our source code for CoInception framework is accessible at https://github.com/anhduy0911/CoInception.

Time series forecasting using historical data has been an interesting and challenging topic, especially when the data is corrupted by missing values. In many industrial problem, it is important to learn the inference function between the auxiliary observations and target variables as it provides additional knowledge when the data is not fully observed. We develop an end-to-end time series model that aims to learn the such inference relation and make a multiple-step ahead forecast. Our framework trains jointly two neural networks, one to learn the feature-wise correlations and the other for the modeling of temporal behaviors. Our model is capable of simultaneously imputing the missing entries and making a multiple-step ahead prediction. The experiments show good overall performance of our framework over existing methods in both imputation and forecasting tasks.

Concept bottleneck models (CBM) are a popular way of creating more interpretable neural networks by having hidden layer neurons correspond to human-understandable concepts. However, existing CBMs and their variants have two crucial limitations: first, they need to collect labeled data for each of the predefined concepts, which is time consuming and labor intensive; second, the accuracy of a CBM is often significantly lower than that of a standard neural network, especially on more complex datasets. This poor performance creates a barrier for adopting CBMs in practical real world applications. Motivated by these challenges, we propose Label-free CBM which is a novel framework to transform any neural network into an interpretable CBM without labeled concept data, while retaining a high accuracy. Our Label-free CBM has many advantages, it is: scalable - we present the first CBM scaled to ImageNet, efficient - creating a CBM takes only a few hours even for very large datasets, and automated - training it for a new dataset requires minimal human effort. Our code is available at https://github.com/Trustworthy-ML-Lab/Label-free-CBM. Finally, in Appendix B we conduct a large scale user evaluation of the interpretability of our method., Comment: Published at ICLR 2023. New v2(5 June 2023): added crowdsourced human study in Appendix B

The International Pulsar Timing Array 2nd data release is the combination of datasets from worldwide collaborations. In this study, we search for continuous waves: gravitational wave signals produced by individual supermassive black hole binaries in the local universe. We consider binaries on circular orbits and neglect the evolution of orbital frequency over the observational span. We find no evidence for such signals and set sky averaged 95% upper limits on their amplitude h 95 . The most sensitive frequency is 10nHz with h 95 = 9.1 10-15 . We achieved the best upper limit to date at low and high frequencies of the PTA band thanks to improved effective cadence of observations. In our analysis, we have taken into account the recently discovered common red noise process, which has an impact at low frequencies. We also find that the peculiar noise features present in some pulsars data must be taken into account to reduce the false alarm. We show that using custom noise models is essential in searching for continuous gravitational wave signals and setting the upper limit.

Deep neural networks (DNN) have shown great capacity of modeling a dynamical system; nevertheless, they usually do not obey physics constraints such as conservation laws. This paper proposes a new learning framework named ConCerNet to improve the trustworthiness of the DNN based dynamics modeling to endow the invariant properties. ConCerNet consists of two steps: (i) a contrastive learning method to automatically capture the system invariants (i.e. conservation properties) along the trajectory observations; (ii) a neural projection layer to guarantee that the learned dynamics models preserve the learned invariants. We theoretically prove the functional relationship between the learned latent representation and the unknown system invariant function. Experiments show that our method consistently outperforms the baseline neural networks in both coordinate error and conservation metrics by a large margin. With neural network based parameterization and no dependence on prior knowledge, our method can be extended to complex and large-scale dynamics by leveraging an autoencoder., Comment: Accepted by ICML 2023

Classical differential private DP-SGD implements individual clipping with random subsampling, which forces a mini-batch SGD approach. We provide a general differential private algorithmic framework that goes beyond DP-SGD and allows any possible first order optimizers (e.g., classical SGD and momentum based SGD approaches) in combination with batch clipping, which clips an aggregate of computed gradients rather than summing clipped gradients (as is done in individual clipping). The framework also admits sampling techniques beyond random subsampling such as shuffling. Our DP analysis follows the $f$-DP approach and introduces a new proof technique which allows us to derive simple closed form expressions and to also analyse group privacy. In particular, for $E$ epochs work and groups of size $g$, we show a $\sqrt{g E}$ DP dependency for batch clipping with shuffling., Comment: Update disclaimers

Queueing systems appear in many important real-life applications including communication networks, transportation and manufacturing systems. Reinforcement learning (RL) framework is a suitable model for the queueing control problem where the underlying dynamics are usually unknown and the agent receives little information from the environment to navigate. In this work, we investigate the optimization aspects of the queueing model as a RL environment and provide insight to learn the optimal policy efficiently. We propose a new parameterization of the policy by using the intrinsic properties of queueing network systems. Experiments show good performance of our methods with various load conditions from light to heavy traffic.

Stochastic gradient descent (SGD) algorithm is the method of choice in many machine learning tasks thanks to its scalability and efficiency in dealing with large-scale problems. In this paper, we focus on the shuffling version of SGD which matches the mainstream practical heuristics. We show the convergence to a global solution of shuffling SGD for a class of non-convex functions under over-parameterized settings. Our analysis employs more relaxed non-convex assumptions than previous literature. Nevertheless, we maintain the desired computational complexity as shuffling SGD has achieved in the general convex setting., Comment: The 37th Conference on Neural Information Processing Systems (NeurIPS 2023)

From data collection to photometric fitting and analysis of white dwarfs to generating a white dwarf luminosity function requires numerous Astrophysical, Mathematical and Computational domain knowledge. The steep learning curve makes it difficult to enter the field, and often individuals have to reinvent the wheel to perform identical data reduction and analysis tasks. We have gathered a wide range of publicly available white dwarf cooling models and synthetic photometry to provide a toolkit that allows (1) visualisation of various models, (2) photometric fitting of a white dwarf with or without distance and reddening, and (3) the computing of white dwarf luminosity functions with a choice of initial mass function, main sequence evolution model, star formation history, initial-final mass relation, and white dwarf cooling model. We have recomputed and compared the effective temperature of the white dwarfs from the Gaia EDR3 white dwarf catalogue. The two independent works show excellent agreement in the temperature solutions., Comment: 18 pages, 12 figures, 2 tables. Accepted for publication in RAS Techniques and Instruments

We study the Unbalanced Optimal Transport (UOT) between two measures of possibly different masses with at most $n$ components, where the marginal constraints of standard Optimal Transport (OT) are relaxed via Kullback-Leibler divergence with regularization factor $\tau$. Although only Sinkhorn-based UOT solvers have been analyzed in the literature with the iteration complexity of ${O}\big(\tfrac{\tau \log(n)}{\varepsilon} \log\big(\tfrac{\log(n)}{{\varepsilon}}\big)\big)$ and per-iteration cost of $O(n^2)$ for achieving the desired error $\varepsilon$, their positively dense output transportation plans strongly hinder the practicality. On the other hand, while being vastly used as heuristics for computing UOT in modern deep learning applications and having shown success in sparse OT problem, gradient methods applied to UOT have not been formally studied. In this paper, we propose a novel algorithm based on Gradient Extrapolation Method (GEM-UOT) to find an $\varepsilon$-approximate solution to the UOT problem in $O\big( \kappa \log\big(\frac{\tau n}{\varepsilon}\big) \big)$ iterations with $\widetilde{O}(n^2)$ per-iteration cost, where $\kappa$ is the condition number depending on only the two input measures. Our proof technique is based on a novel dual formulation of the squared $\ell_2$-norm UOT objective, which fills the lack of sparse UOT literature and also leads to a new characterization of approximation error between UOT and OT. To this end, we further present a novel approach of OT retrieval from UOT, which is based on GEM-UOT with fine tuned $\tau$ and a post-process projection step. Extensive experiments on synthetic and real datasets validate our theories and demonstrate the favorable performance of our methods in practice.

In recent years, a proliferation of methods were developed for cooperative multi-agent reinforcement learning (c-MARL). However, the robustness of c-MARL agents against adversarial attacks has been rarely explored. In this paper, we propose to evaluate the robustness of c-MARL agents via a model-based approach, named c-MBA. Our proposed formulation can craft much stronger adversarial state perturbations of c-MARL agents to lower total team rewards than existing model-free approaches. In addition, we propose the first victim-agent selection strategy and the first data-driven approach to define targeted failure states where each of them allows us to develop even stronger adversarial attack without the expert knowledge to the underlying environment. Our numerical experiments on two representative MARL benchmarks illustrate the advantage of our approach over other baselines: our model-based attack consistently outperforms other baselines in all tested environments.

In this paper, we propose Nesterov Accelerated Shuffling Gradient (NASG), a new algorithm for the convex finite-sum minimization problems. Our method integrates the traditional Nesterov's acceleration momentum with different shuffling sampling schemes. We show that our algorithm has an improved rate of $\mathcal{O}(1/T)$ using unified shuffling schemes, where $T$ is the number of epochs. This rate is better than that of any other shuffling gradient methods in convex regime. Our convergence analysis does not require an assumption on bounded domain or a bounded gradient condition. For randomized shuffling schemes, we improve the convergence bound further. When employing some initial condition, we show that our method converges faster near the small neighborhood of the solution. Numerical simulations demonstrate the efficiency of our algorithm.

Deep neural networks (DNNs) have shown great success in many machine learning tasks. Their training is challenging since the loss surface of the network architecture is generally non-convex, or even non-smooth. How and under what assumptions is guaranteed convergence to a \textit{global} minimum possible? We propose a reformulation of the minimization problem allowing for a new recursive algorithmic framework. By using bounded style assumptions, we prove convergence to an $\varepsilon$-(global) minimum using $\mathcal{\tilde{O}}(1/\varepsilon^3)$ gradient computations. Our theoretical foundation motivates further study, implementation, and optimization of the new algorithmic framework and further investigation of its non-standard bounded style assumptions. This new direction broadens our understanding of why and under what circumstances training of a DNN converges to a global minimum.

In this paper, we propose the StepDIRECT algorithm for derivative-free optimization (DFO), in which the black-box objective function has a stepwise landscape. Our framework is based on the well-known DIRECT algorithm. By incorporating the local variability to explore the flatness, we provide a new criterion to select the potentially optimal hyper-rectangles. In addition, we introduce a stochastic local search algorithm performing on potentially optimal hyper-rectangles to improve the solution quality and convergence speed. Global convergence of the StepDIRECT algorithm is provided. Numerical experiments on optimization for random forest models and hyper-parameter tuning are presented to support the efficacy of our algorithm. The proposed StepDIRECT algorithm shows competitive performance results compared with other state-of-the-art baseline DFO methods including the original DIRECT algorithm.

We searched for an isotropic stochastic gravitational wave background in the second data release of the International Pulsar Timing Array, a global collaboration synthesizing decadal-length pulsar-timing campaigns in North America, Europe, and Australia. In our reference search for a power law strain spectrum of the form $h_c = A(f/1\,\mathrm{yr}^{-1})^{\alpha}$, we found strong evidence for a spectrally-similar low-frequency stochastic process of amplitude $A = 3.8^{+6.3}_{-2.5}\times10^{-15}$ and spectral index $\alpha = -0.5 \pm 0.5$, where the uncertainties represent 95\% credible regions, using information from the auto- and cross-correlation terms between the pulsars in the array. For a spectral index of $\alpha = -2/3$, as expected from a population of inspiralling supermassive black hole binaries, the recovered amplitude is $A = 2.8^{+1.2}_{-0.8}\times10^{-15}$. Nonetheless, no significant evidence of the Hellings-Downs correlations that would indicate a gravitational-wave origin was found. We also analyzed the constituent data from the individual pulsar timing arrays in a consistent way, and clearly demonstrate that the combined international data set is more sensitive. Furthermore, we demonstrate that this combined data set produces comparable constraints to recent single-array data sets which have more data than the constituent parts of the combination. Future international data releases will deliver increased sensitivity to gravitational wave radiation, and significantly increase the detection probability., Comment: 17 pages, 12 figures, accepted in MNRAS

Clustering is a popular unsupervised learning tool often used to discover groups within a larger population such as customer segments, or patient subtypes. However, despite its use as a tool for subgroup discovery and description - few state-of-the-art algorithms provide any rationale or description behind the clusters found. We propose a novel approach for interpretable clustering that both clusters data points and constructs polytopes around the discovered clusters to explain them. Our framework allows for additional constraints on the polytopes - including ensuring that the hyperplanes constructing the polytope are axis-parallel or sparse with integer coefficients. We formulate the problem of constructing clusters via polytopes as a Mixed-Integer Non-Linear Program (MINLP). To solve our formulation we propose a two phase approach where we first initialize clusters and polytopes using alternating minimization, and then use coordinate descent to boost clustering performance. We benchmark our approach on a suite of synthetic and real world clustering problems, where our algorithm outperforms state of the art interpretable and non-interpretable clustering algorithms., Comment: Accepted to the 36th AAAI Conference on Artificial Intelligence (AAAI 2022)

We present the photometric analysis of Gaia19bld, a high-magnification ($A\approx60$) microlensing event located in the southern Galactic plane, which exhibited finite source and microlensing parallax effects. Due to a prompt detection by the Gaia satellite and the very high brightness of $I = 9.05~$mag at the peak, it was possible to collect a complete and unique set of multi-channel follow-up observations, which allowed us to determine all parameters vital for the characterisation of the lens and the source in the microlensing event. Gaia19bld was discovered by the Gaia satellite and was subsequently intensively followed up with a network of ground-based observatories and the Spitzer Space Telescope. We collected multiple high-resolution spectra with Very Large Telescope (VLT)/X-Shooter to characterise the source star. The event was also observed with VLT Interferometer (VLTI)/PIONIER during the peak. Here we focus on the photometric observations and model the light curve composed of data from Gaia, Spitzer, and multiple optical, ground-based observatories. We find the best-fitting solution with parallax and finite source effects. We derived the limit on the luminosity of the lens based on the blended light model and spectroscopic distance. We compute the mass of the lens to be $1.13 \pm 0.03~M_{\odot}$ and derive its distance to be $5.52^{+0.35}_{-0.64}~\mathrm{kpc}$. The lens is likely a main sequence star, however its true nature has yet to be verified by future high-resolution observations. Our results are consistent with interferometric measurements of the angular Einstein radius, emphasising that interferometry can be a new channel for determining the masses of objects that would otherwise remain undetectable, including stellar-mass black holes., Comment: accepted to Astronomy&Astrophysics

Recent research shows that the dynamics of an infinitely wide neural network (NN) trained by gradient descent can be characterized by Neural Tangent Kernel (NTK) \citep{jacot2018neural}. Under the squared loss, the infinite-width NN trained by gradient descent with an infinitely small learning rate is equivalent to kernel regression with NTK \citep{arora2019exact}. However, the equivalence is only known for ridge regression currently \citep{arora2019harnessing}, while the equivalence between NN and other kernel machines (KMs), e.g. support vector machine (SVM), remains unknown. Therefore, in this work, we propose to establish the equivalence between NN and SVM, and specifically, the infinitely wide NN trained by soft margin loss and the standard soft margin SVM with NTK trained by subgradient descent. Our main theoretical results include establishing the equivalences between NNs and a broad family of $\ell_2$ regularized KMs with finite-width bounds, which cannot be handled by prior work, and showing that every finite-width NN trained by such regularized loss functions is approximately a KM. Furthermore, we demonstrate our theory can enable three practical applications, including (i) \textit{non-vacuous} generalization bound of NN via the corresponding KM; (ii) \textit{non-trivial} robustness certificate for the infinite-width NN (while existing robustness verification methods would provide vacuous bounds); (iii) intrinsically more robust infinite-width NNs than those from previous kernel regression. Our code for the experiments is available at \url{https://github.com/leslie-CH/equiv-nn-svm}., Comment: 35th Conference on Neural Information Processing Systems (NeurIPS 2021)

In many machine learning tasks, models are trained to predict structure data such as graphs. For example, in natural language processing, it is very common to parse texts into dependency trees or abstract meaning representation (AMR) graphs. On the other hand, ensemble methods combine predictions from multiple models to create a new one that is more robust and accurate than individual predictions. In the literature, there are many ensembling techniques proposed for classification or regression problems, however, ensemble graph prediction has not been studied thoroughly. In this work, we formalize this problem as mining the largest graph that is the most supported by a collection of graph predictions. As the problem is NP-Hard, we propose an efficient heuristic algorithm to approximate the optimal solution. To validate our approach, we carried out experiments in AMR parsing problems. The experimental results demonstrate that the proposed approach can combine the strength of state-of-the-art AMR parsers to create new predictions that are more accurate than any individual models in five standard benchmark datasets., Comment: Published at NeurIPS 2021