Ensemble transform Kalman filtering (ETKF) data assimilation is often used to combine available observations with numerical simulations to obtain statistically accurate and reliable state representations in dynamical systems. However, it is well known that the commonly used Gaussian distribution assumption introduces biases for state variables that admit discontinuous profiles, which are prevalent in nonlinear partial differential equations. This investigation designs a new structurally informed non-Gaussian prior that exploits statistical information from the simulated state variables. In particular, we construct a new weighting matrix based on the second moment of the gradient information of the state variable to replace the prior covariance matrix used for model/data compromise in the ETKF data assimilation framework. We further adapt our weighting matrix to include information in discontinuity regions via a clustering technique. Our numerical experiments demonstrate that this new approach yields more accurate estimates than those obtained using ETKF on shallow water equations, even when ETKF is enhanced with inflation and localization techniques.
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Continual Federated Learning (CFL) combines Federated Learning (FL), the decentralized learning of a central model on a number of client devices that may not communicate their data, and Continual Learning (CL), the learning of a model from a continual stream of data without keeping the entire history. In CL, the main challenge is \textit{forgetting} what was learned from past data. While replay-based algorithms that keep a small pool of past training data are effective to reduce forgetting, only simple replay sample selection strategies have been applied to CFL in prior work, and no previous work has explored coordination among clients for better sample selection. To bridge this gap, we adapt a replay sample selection objective based on loss gradient diversity to CFL and propose a new relaxation-based selection of samples to optimize the objective. Next, we propose a practical algorithm to coordinate gradient-based replay sample selection across clients without communicating private data. We benchmark our coordinated and uncoordinated replay sample selection algorithms against random sampling-based baselines with language models trained on a large scale de-identified real-world text dataset. We show that gradient-based sample selection methods both boost performance and reduce forgetting compared to random sampling methods, with our coordination method showing gains early in the low replay size regime (when the budget for storing past data is small).
Anomaly Detection (AD) is a critical task that involves identifying observations that do not conform to a learned model of normality. Prior work in deep AD is predominantly based on a familiarity hypothesis, where familiar features serve as the reference in a pre-trained embedding space. While this strategy has proven highly successful, it turns out that it causes consistent false negatives when anomalies consist of truly novel features that are not well captured by the pre-trained encoding. We propose a novel approach to AD using explainability to capture novel features as unexplained observations in the input space. We achieve strong performance across a wide range of anomaly benchmarks by combining similarity and novelty in a hybrid approach. Our approach establishes a new state-of-the-art across multiple benchmarks, handling diverse anomaly types while eliminating the need for expensive background models and dense matching. In particular, we show that by taking account of novel features, we reduce false negative anomalies by up to 40% on challenging benchmarks compared to the state-of-the-art. Our method gives visually inspectable explanations for pixel-level anomalies.
Topic segmentation is critical for obtaining structured documents and improving downstream tasks such as information retrieval. Due to its ability of automatically exploring clues of topic shift from abundant labeled data, recent supervised neural models have greatly promoted the development of long document topic segmentation, but leaving the deeper relationship between coherence and topic segmentation underexplored. Therefore, this paper enhances the ability of supervised models to capture coherence from both logical structure and semantic similarity perspectives to further improve the topic segmentation performance, proposing Topic-aware Sentence Structure Prediction (TSSP) and Contrastive Semantic Similarity Learning (CSSL). Specifically, the TSSP task is proposed to force the model to comprehend structural information by learning the original relations between adjacent sentences in a disarrayed document, which is constructed by jointly disrupting the original document at topic and sentence levels. Moreover, we utilize inter- and intra-topic information to construct contrastive samples and design the CSSL objective to ensure that the sentences representations in the same topic have higher similarity, while those in different topics are less similar. Extensive experiments show that the Longformer with our approach significantly outperforms old state-of-the-art (SOTA) methods. Our approach improve $F_1$ of old SOTA by 3.42 (73.74 -> 77.16) and reduces $P_k$ by 1.11 points (15.0 -> 13.89) on WIKI-727K and achieves an average relative reduction of 4.3% on $P_k$ on WikiSection. The average relative $P_k$ drop of 8.38% on two out-of-domain datasets also demonstrates the robustness of our approach.
A novel recurrence formula for moments with respect to M\"{u}ntz-Legendre polynomials is proposed and applied to construct a numerical method for solving generalized Gauss quadratures with power function weight for M\"{u}ntz systems. These quadrature rules exhibit several properties similar to the classical Gaussian quadratures for polynomial systems, including positive weights, rapid convergence, and others. They are applicable to a wide range of functions, including smooth functions and functions with endpoint singularities, commonly found in integral equations with singular kernels, complex analysis, potential theory, and other areas.
Fitting generative models to sequential data typically involves two recursive computations through time, one forward and one backward. The latter could be a computation of the loss gradient (as in backpropagation through time), or an inference algorithm (as in the RTS/Kalman smoother). The backward pass in particular is computationally expensive (since it is inherently serial and cannot exploit GPUs), and difficult to map onto biological processes. Work-arounds have been proposed; here we explore a very different one: requiring the generative model to learn the joint distribution over current and previous states, rather than merely the transition probabilities. We show on toy datasets that different architectures employing this principle can learn aspects of the data typically requiring the backward pass.
All-digital massive multiuser (MU) multiple-input multiple-output (MIMO) at millimeter-wave (mmWave) frequencies is a promising technology for next-generation wireless systems. Low-resolution analog-to-digital converters (ADCs) can be utilized to reduce the power consumption of all-digital basestation (BS) designs. However, simultaneously transmitting user equipments (UEs) with vastly different BS-side receive powers either drown weak UEs in quantization noise or saturate the ADCs. To address this issue, we propose high dynamic range (HDR) MIMO, a new paradigm that enables simultaneous reception of strong and weak UEs with low-resolution ADCs. HDR MIMO combines an adaptive analog spatial transform with digital equalization: The spatial transform focuses strong UEs on a subset of ADCs in order to mitigate quantization and saturation artifacts; digital equalization is then used for data detection. We demonstrate the efficacy of HDR MIMO in a massive MU-MIMO mmWave scenario that uses Householder reflections as spatial transform.
Sequential transfer optimization (STO), which aims to improve the optimization performance on a task of interest by exploiting the knowledge captured from several previously-solved optimization tasks stored in a database, has been gaining increasing research attention over the years. However, despite the remarkable advances in algorithm design, the development of a systematic benchmark suite for comprehensive comparisons of STO algorithms received far less attention. Existing test problems are either simply generated by assembling other benchmark functions or extended from specific practical problems with limited scalability. The relationships between the optimal solutions of the source and target tasks in these problems are also often manually configured, limiting their ability to model different similarity relationships presented in real-world problems. Consequently, the good performance achieved by an algorithm on these problems might be biased and hard to be generalized to other problems. In light of the above, in this study, we first introduce four concepts for characterizing STO problems and present an important problem feature, namely similarity distribution, which quantitatively delineates the relationship between the optima of the source and target tasks. Then, we present the general design guidelines of STO problems and a particular STO problem generator with good scalability. Specifically, the similarity distribution of a problem can be easily customized, enabling a continuous spectrum of representation of the diverse similarity relationships of real-world problems. Lastly, a benchmark suite with 12 STO problems featured by a variety of customized similarity relationships is developed using the proposed generator. The source code of the problem generator is available at //github.com/XmingHsueh/STOP-G.
Bayesian hypothesis testing leverages posterior probabilities, Bayes factors, or credible intervals to assess characteristics that summarize data. We propose a framework for power curve approximation with such hypothesis tests that assumes data are generated using statistical models with fixed parameters for the purposes of sample size determination. We present a fast approach to explore the sampling distribution of posterior probabilities when the conditions for the Bernstein-von Mises theorem are satisfied. We extend that approach to facilitate targeted sampling from the approximate sampling distribution of posterior probabilities for each sample size explored. These sampling distributions are used to construct power curves for various types of posterior analyses. Our resulting method for power curve approximation is orders of magnitude faster than conventional power curve estimation for Bayesian hypothesis tests. We also prove the consistency of the corresponding power estimates and sample size recommendations under certain conditions.
Algebraic data types (ADTs) are a construct classically found in functional programming languages that capture data structures like enumerated types, lists, and trees. In recent years, interest in ADTs has increased. For example, popular programming languages, like Python, have added support for ADTs. Automated reasoning about ADTs can be done using satisfiability modulo theories (SMT) solving, an extension of the Boolean satisfiability problem with constraints over first-order structures. Unfortunately, SMT solvers that support ADTs do not scale as state-of-the-art approaches all use variations of the same \emph{lazy} approach. In this paper, we present an SMT solver that takes a fundamentally different approach, an \emph{eager} approach. Specifically, our solver reduces ADT queries to a simpler logical theory, uninterpreted functions (UF), and then uses an existing solver on the reduced query. We prove the soundness and completeness of our approach and demonstrate that it outperforms the state-of-theart on existing benchmarks, as well as a new, more challenging benchmark set from the planning domain.
Causality can be described in terms of a structural causal model (SCM) that carries information on the variables of interest and their mechanistic relations. For most processes of interest the underlying SCM will only be partially observable, thus causal inference tries to leverage any exposed information. Graph neural networks (GNN) as universal approximators on structured input pose a viable candidate for causal learning, suggesting a tighter integration with SCM. To this effect we present a theoretical analysis from first principles that establishes a novel connection between GNN and SCM while providing an extended view on general neural-causal models. We then establish a new model class for GNN-based causal inference that is necessary and sufficient for causal effect identification. Our empirical illustration on simulations and standard benchmarks validate our theoretical proofs.
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