We address the problem of monitoring a set of binary stochastic processes and generating an alert when the number of anomalies among them exceeds a threshold. For this, the decision-maker selects and probes a subset of the processes to obtain noisy estimates of their states (normal or anomalous). Based on the received observations, the decisionmaker first determines whether to declare that the number of anomalies has exceeded the threshold or to continue taking observations. When the decision is to continue, it then decides whether to collect observations at the next time instant or defer it to a later time. If it chooses to collect observations, it further determines the subset of processes to be probed. To devise this three-step sequential decision-making process, we use a Bayesian formulation wherein we learn the posterior probability on the states of the processes. Using the posterior probability, we construct a Markov decision process and solve it using deep actor-critic reinforcement learning. Via numerical experiments, we demonstrate the superior performance of our algorithm compared to the traditional model-based algorithms.
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Processing 是一門開源編程語言和與之配套的集成開發環境（IDE）的名稱。Processing 在電子藝術和視覺設計社區被用來教授編程基礎，并運用于大量的新媒體和互動藝術作品中。
We present a novel form of Fourier analysis, and associated signal processing concepts, for signals (or data) indexed by edge-weighted directed acyclic graphs (DAGs). This means that our Fourier basis yields an eigendecomposition of a suitable notion of shift and convolution operators that we define. DAGs are the common model to capture causal relationships between data values and in this case our proposed Fourier analysis relates data with its causes under a linearity assumption that we define. The definition of the Fourier transform requires the transitive closure of the weighted DAG for which several forms are possible depending on the interpretation of the edge weights. Examples include level of influence, distance, or pollution distribution. Our framework is different from prior GSP: it is specific to DAGs and leverages, and extends, the classical theory of Moebius inversion from combinatorics. For a prototypical application we consider DAGs modeling dynamic networks in which edges change over time. Specifically, we model the spread of an infection on such a DAG obtained from real-world contact tracing data and learn the infection signal from samples assuming sparsity in the Fourier domain.
Spread spectrum multiple access systems demand minimum possible cross-correlation between the sequences within a set of sequences having good auto-correlation properties. Through a connection between generalised Frank sequences and Florentine arrays, we present a family of perfect sequences with low cross-correlation having a larger family size, compared with previous works. In particular, the family size can be equal to the square root of the period when the period of the perfect sequences is even. In contrast, the number of the perfect sequences of even period with low cross-correlation is equal to one in all previous works.
Arctic amplification has altered the climate patterns both regionally and globally, resulting in more frequent and more intense extreme weather events in the past few decades. The essential part of Arctic amplification is the unprecedented sea ice loss as demonstrated by satellite observations. Accurately forecasting Arctic sea ice from sub-seasonal to seasonal scales has been a major research question with fundamental challenges at play. In addition to physics-based Earth system models, researchers have been applying multiple statistical and machine learning models for sea ice forecasting. Looking at the potential of data-driven approaches to study sea ice variations, we propose MT-IceNet - a UNet based spatial and multi-temporal (MT) deep learning model for forecasting Arctic sea ice concentration (SIC). The model uses an encoder-decoder architecture with skip connections and processes multi-temporal input streams to regenerate spatial maps at future timesteps. Using bi-monthly and monthly satellite retrieved sea ice data from NSIDC as well as atmospheric and oceanic variables from ERA5 reanalysis product during 1979-2021, we show that our proposed model provides promising predictive performance for per-pixel SIC forecasting with up to 60% decrease in prediction error for a lead time of 6 months as compared to its state-of-the-art counterparts.
Search query variation poses a challenge in e-commerce search, as equivalent search intents can be expressed through different queries with surface-level differences. This paper introduces a framework to recognize and leverage query equivalence to enhance searcher and business outcomes. The proposed approach addresses three key problems: mapping queries to vector representations of search intent, identifying nearest neighbor queries expressing equivalent or similar intent, and optimizing for user or business objectives. The framework utilizes both surface similarity and behavioral similarity to determine query equivalence. Surface similarity involves canonicalizing queries based on word inflection, word order, compounding, and noise words. Behavioral similarity leverages historical search behavior to generate vector representations of query intent. An offline process is used to train a sentence similarity model, while an online nearest neighbor approach supports processing of unseen queries. Experimental evaluations demonstrate the effectiveness of the proposed approach, outperforming popular sentence transformer models and achieving a Pearson correlation of 0.85 for query similarity. The results highlight the potential of leveraging historical behavior data and training models to recognize and utilize query equivalence in e-commerce search, leading to improved user experiences and business outcomes. Further advancements and benchmark datasets are encouraged to facilitate the development of solutions for this critical problem in the e-commerce domain.
Understanding how well a deep generative model captures a distribution of high-dimensional data remains an important open challenge. It is especially difficult for certain model classes, such as Generative Adversarial Networks and Diffusion Models, whose models do not admit exact likelihoods. In this work, we demonstrate that generalized empirical likelihood (GEL) methods offer a family of diagnostic tools that can identify many deficiencies of deep generative models (DGMs). We show, with appropriate specification of moment conditions, that the proposed method can identify which modes have been dropped, the degree to which DGMs are mode imbalanced, and whether DGMs sufficiently capture intra-class diversity. We show how to combine techniques from Maximum Mean Discrepancy and Generalized Empirical Likelihood to create not only distribution tests that retain per-sample interpretability, but also metrics that include label information. We find that such tests predict the degree of mode dropping and mode imbalance up to 60% better than metrics such as improved precision/recall. We provide an implementation at //github.com/deepmind/understanding_deep_generative_models_with_generalized_empirical_likelihood/.
We introduce the problem of phone classification in the context of speech recognition, and explore several sets of local spectro-temporal features that can be used for phone classification. In particular, we present some preliminary results for phone classification using two sets of features that are commonly used for object detection: Haar features and SVM-classified Histograms of Gradients (HoG).
Efficient differential equation solvers have significantly reduced the sampling time of diffusion models (DMs) while retaining high sampling quality. Among these solvers, exponential integrators (EI) have gained prominence by demonstrating state-of-the-art performance. However, existing high-order EI-based sampling algorithms rely on degenerate EI solvers, resulting in inferior error bounds and reduced accuracy in contrast to the theoretically anticipated results under optimal settings. This situation makes the sampling quality extremely vulnerable to seemingly innocuous design choices such as timestep schedules. For example, an inefficient timestep scheduler might necessitate twice the number of steps to achieve a quality comparable to that obtained through carefully optimized timesteps. To address this issue, we reevaluate the design of high-order differential solvers for DMs. Through a thorough order analysis, we reveal that the degeneration of existing high-order EI solvers can be attributed to the absence of essential order conditions. By reformulating the differential equations in DMs and capitalizing on the theory of exponential integrators, we propose refined EI solvers that fulfill all the order conditions, which we designate as Refined Exponential Solver (RES). Utilizing these improved solvers, RES exhibits more favorable error bounds theoretically and achieves superior sampling efficiency and stability in practical applications. For instance, a simple switch from the single-step DPM-Solver++ to our order-satisfied RES solver when Number of Function Evaluations (NFE) $=9$, results in a reduction of numerical defects by $25.2\%$ and FID improvement of $25.4\%$ (16.77 vs 12.51) on a pre-trained ImageNet diffusion model.
We consider statistical inference of equality-constrained stochastic nonlinear optimization problems. We develop a fully online stochastic sequential quadratic programming (StoSQP) method to solve the problems, which can be regarded as applying Newton's method to the first-order optimality conditions (i.e., the KKT conditions). Motivated by recent designs of numerical second-order methods, we allow StoSQP to adaptively select any random stepsize $\bar{\alpha}_t$, as long as $\beta_t\leq \bar{\alpha}_t \leq \beta_t+\chi_t$, for some control sequences $\beta_t$ and $\chi_t=o(\beta_t)$. To reduce the dominant computational cost of second-order methods, we additionally allow StoSQP to inexactly solve quadratic programs via efficient randomized iterative solvers that utilize sketching techniques. Notably, we do not require the approximation error to diminish as iteration proceeds. For the developed method, we show that under mild assumptions (i) computationally, it can take at most $O(1/\epsilon^4)$ iterations (same as samples) to attain $\epsilon$-stationarity; (ii) statistically, its primal-dual sequence $1/\sqrt{\beta_t}\cdot (x_t - x^\star, \lambda_t - \lambda^\star)$ converges to a mean-zero Gaussian distribution with a nontrivial covariance matrix depending on the underlying sketching distribution. Additionally, we establish the almost-sure convergence rate of the iterate $(x_t, \lambda_t)$ along with the Berry-Esseen bound; the latter quantitatively measures the convergence rate of the distribution function. We analyze a plug-in limiting covariance matrix estimator, and demonstrate the performance of the method both on benchmark nonlinear problems in CUTEst test set and on linearly/nonlinearly constrained regression problems.
Residual networks (ResNets) have displayed impressive results in pattern recognition and, recently, have garnered considerable theoretical interest due to a perceived link with neural ordinary differential equations (neural ODEs). This link relies on the convergence of network weights to a smooth function as the number of layers increases. We investigate the properties of weights trained by stochastic gradient descent and their scaling with network depth through detailed numerical experiments. We observe the existence of scaling regimes markedly different from those assumed in neural ODE literature. Depending on certain features of the network architecture, such as the smoothness of the activation function, one may obtain an alternative ODE limit, a stochastic differential equation or neither of these. These findings cast doubts on the validity of the neural ODE model as an adequate asymptotic description of deep ResNets and point to an alternative class of differential equations as a better description of the deep network limit.
We introduce a multi-task setup of identifying and classifying entities, relations, and coreference clusters in scientific articles. We create SciERC, a dataset that includes annotations for all three tasks and develop a unified framework called Scientific Information Extractor (SciIE) for with shared span representations. The multi-task setup reduces cascading errors between tasks and leverages cross-sentence relations through coreference links. Experiments show that our multi-task model outperforms previous models in scientific information extraction without using any domain-specific features. We further show that the framework supports construction of a scientific knowledge graph, which we use to analyze information in scientific literature.
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