We consider the problem of estimating the spectrum of a symmetric bounded entry (not necessarily PSD) matrix via entrywise sampling. This problem was introduced by [Bhattacharjee, Dexter, Drineas, Musco, Ray '22], where it was shown that one can obtain an $\epsilon n$ additive approximation to all eigenvalues of $A$ by sampling a principal submatrix of dimension $\frac{\text{poly}(\log n)}{\epsilon^3}$. We improve their analysis by showing that it suffices to sample a principal submatrix of dimension $\tilde{O}(\frac{1}{\epsilon^2})$ (with no dependence on $n$). This matches known lower bounds and therefore resolves the sample complexity of this problem up to $\log\frac{1}{\epsilon}$ factors. Using similar techniques, we give a tight $\tilde{O}(\frac{1}{\epsilon^2})$ bound for obtaining an additive $\epsilon\|A\|_F$ approximation to the spectrum of $A$ via squared row-norm sampling, improving on the previous best $\tilde{O}(\frac{1}{\epsilon^{8}})$ bound. We also address the problem of approximating the top eigenvector for a bounded entry, PSD matrix $A.$ In particular, we show that sampling $O(\frac{1}{\epsilon})$ columns of $A$ suffices to produce a unit vector $u$ with $u^T A u \geq \lambda_1(A) - \epsilon n$. This matches what one could achieve via the sampling bound of [Musco, Musco'17] for the special case of approximating the top eigenvector, but does not require adaptivity. As additional applications, we observe that our sampling results can be used to design a faster eigenvalue estimation sketch for dense matrices resolving a question of [Swartworth, Woodruff'23], and can also be combined with [Musco, Musco'17] to achieve $O(1/\epsilon^3)$ (adaptive) sample complexity for approximating the spectrum of a bounded entry PSD matrix to $\epsilon n$ additive error.
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Although the current different types of SAM adaptation methods have achieved promising performance for various downstream tasks, such as prompt-based ones and adapter-based ones, most of them belong to the one-step adaptation paradigm. In real-world scenarios, we are generally confronted with the dynamic scenario where the data comes in a streaming manner. Driven by the practical need, in this paper, we first propose a novel Continual SAM adaptation (CoSAM) benchmark with 8 different task domains and carefully analyze the limitations of the existing SAM one-step adaptation methods in the continual segmentation scenario. Then we propose a novel simple-yet-effective Mixture of Domain Adapters (MoDA) algorithm which utilizes the Global Feature Tokens (GFT) and Global Assistant Tokens (GAT) modules to help the SAM encoder extract well-separated features for different task domains, and then provide the accurate task-specific information for continual learning. Extensive experiments demonstrate that our proposed MoDA obviously surpasses the existing classic continual learning methods, as well as prompt-based and adapter-based approaches for continual segmentation. Moreover, after sequential learning on the CoSAM benchmark with diverse data distributions, our MoDA maintains highly competitive results in the natural image domain, approaching the zero-shot performance of the original SAM, demonstrating its superior capability in knowledge preservation. Notably, the proposed MoDA can be seamlessly integrated into various one-step adaptation methods of SAM, which can consistently bring obvious performance gains. Code is available at \url{//github.com/yangjl1215/CoSAM}
A new online multiple testing procedure is described in the context of anomaly detection, which controls the False Discovery Rate (FDR). An accurate anomaly detector must control the false positive rate at a prescribed level while keeping the false negative rate as low as possible. However in the online context, such a constraint remains highly challenging due to the usual lack of FDR control: the online framework makes it impossible to use classical multiple testing approaches such as the Benjamini-Hochberg (BH) procedure, which would require knowing the entire time series. The developed strategy relies on exploiting the local control of the ``modified FDR'' (mFDR) criterion. It turns out that the local control of mFDR enables global control of the FDR over the full series up to additional modifications of the multiple testing procedures. An important ingredient in this control is the cardinality of the calibration dataset used to compute the empirical p-values. A dedicated strategy for tuning this parameter is designed for achieving the prescribed FDR control over the entire time series. The good statistical performance of the full strategy is analyzed by theoretical guarantees. Its practical behavior is assessed by several simulation experiments which support our conclusions.
Information Retrieval (IR) methods aim to identify documents relevant to a query, which have been widely applied in various natural language tasks. However, existing approaches typically consider only the textual content within documents, overlooking the fact that documents can contain multiple modalities, including images and tables. Also, they often segment each long document into multiple discrete passages for embedding, which prevents them from capturing the overall document context and interactions between paragraphs. To address these two challenges, we propose a method that holistically embeds documents interleaved with multiple modalities by leveraging the capability of recent vision-language models that enable the processing and integration of text, images, and tables into a unified format and representation. Moreover, to mitigate the information loss from segmenting documents into passages, instead of representing and retrieving passages individually, we further merge the representations of segmented passages into one single document representation, while we additionally introduce a reranking strategy to decouple and identify the relevant passage within the document if necessary. Then, through extensive experiments on diverse IR scenarios considering both the textual and multimodal queries, we show that our approach substantially outperforms relevant baselines, thanks to the consideration of the multimodal information within documents.
Hypertree decompositions provide a way to evaluate Conjunctive Queries (CQs) in polynomial time, where the exponent of this polynomial is determined by the width of the decomposition. In theory, the goal of efficient CQ evaluation therefore has to be a minimisation of the width. However, in practical settings, it turns out that there are also other properties of a decomposition that influence the performance of query evaluation. It is therefore of interest to restrict the computation of decompositions by constraints and to guide this computation by preferences. To this end, we propose a novel framework based on candidate tree decompositions, which allows us to introduce soft hypertree width (shw). This width measure is a relaxation of hypertree width (hw); it is never greater than hw and, in some cases, shw may actually be lower than hw. ost importantly, shw preserves the tractability of deciding if a given CQ is below some fixed bound, while offering more algorithmic flexibility. In particular, it provides a natural way to incorporate preferences A prototype implementation and preliminary experiments confirm that this novel framework can indeed have a practical impact on query evaluation.
A challenge in high-dimensional inverse problems is developing iterative solvers to find the accurate solution of regularized optimization problems with low computational cost. An important example is computed tomography (CT) where both image and data sizes are large and therefore the forward model is costly to evaluate. Since several years algorithms from stochastic optimization are used for tomographic image reconstruction with great success by subsampling the data. Here we propose a novel way how stochastic optimization can be used to speed up image reconstruction by means of image domain sketching such that at each iteration an image of different resolution is being used. Hence, we coin this algorithm ImaSk. By considering an associated saddle-point problem, we can formulate ImaSk as a gradient-based algorithm where the gradient is approximated in the same spirit as the stochastic average gradient am\'elior\'e (SAGA) and uses at each iteration one of these multiresolution operators at random. We prove that ImaSk is linearly converging for linear forward models with strongly convex regularization functions. Numerical simulations on CT show that ImaSk is effective and increasing the number of multiresolution operators reduces the computational time to reach the modeled solution.
We propose a novel formalism for describing Structural Causal Models (SCMs) as fixed-point problems on causally ordered variables, eliminating the need for Directed Acyclic Graphs (DAGs), and establish the weakest known conditions for their unique recovery given the topological ordering (TO). Based on this, we design a two-stage causal generative model that first infers in a zero-shot manner a valid TO from observations, and then learns the generative SCM on the ordered variables. To infer TOs, we propose to amortize the learning of TOs on synthetically generated datasets by sequentially predicting the leaves of graphs seen during training. To learn SCMs, we design a transformer-based architecture that exploits a new attention mechanism enabling the modeling of causal structures, and show that this parameterization is consistent with our formalism. Finally, we conduct an extensive evaluation of each method individually, and show that when combined, our model outperforms various baselines on generated out-of-distribution problems. The code is available on \href{//github.com/microsoft/causica/tree/main/research_experiments/fip}{Github}.
Feature selection is crucial for pinpointing relevant features in high-dimensional datasets, mitigating the 'curse of dimensionality,' and enhancing machine learning performance. Traditional feature selection methods for classification use data from all classes to select features for each class. This paper explores feature selection methods that select features for each class separately, using class models based on low-rank generative methods and introducing a signal-to-noise ratio (SNR) feature selection criterion. This novel approach has theoretical true feature recovery guarantees under certain assumptions and is shown to outperform some existing feature selection methods on standard classification datasets.
Humans perceive the world by concurrently processing and fusing high-dimensional inputs from multiple modalities such as vision and audio. Machine perception models, in stark contrast, are typically modality-specific and optimised for unimodal benchmarks, and hence late-stage fusion of final representations or predictions from each modality (`late-fusion') is still a dominant paradigm for multimodal video classification. Instead, we introduce a novel transformer based architecture that uses `fusion bottlenecks' for modality fusion at multiple layers. Compared to traditional pairwise self-attention, our model forces information between different modalities to pass through a small number of bottleneck latents, requiring the model to collate and condense the most relevant information in each modality and only share what is necessary. We find that such a strategy improves fusion performance, at the same time reducing computational cost. We conduct thorough ablation studies, and achieve state-of-the-art results on multiple audio-visual classification benchmarks including Audioset, Epic-Kitchens and VGGSound. All code and models will be released.
Recent contrastive representation learning methods rely on estimating mutual information (MI) between multiple views of an underlying context. E.g., we can derive multiple views of a given image by applying data augmentation, or we can split a sequence into views comprising the past and future of some step in the sequence. Contrastive lower bounds on MI are easy to optimize, but have a strong underestimation bias when estimating large amounts of MI. We propose decomposing the full MI estimation problem into a sum of smaller estimation problems by splitting one of the views into progressively more informed subviews and by applying the chain rule on MI between the decomposed views. This expression contains a sum of unconditional and conditional MI terms, each measuring modest chunks of the total MI, which facilitates approximation via contrastive bounds. To maximize the sum, we formulate a contrastive lower bound on the conditional MI which can be approximated efficiently. We refer to our general approach as Decomposed Estimation of Mutual Information (DEMI). We show that DEMI can capture a larger amount of MI than standard non-decomposed contrastive bounds in a synthetic setting, and learns better representations in a vision domain and for dialogue generation.
High spectral dimensionality and the shortage of annotations make hyperspectral image (HSI) classification a challenging problem. Recent studies suggest that convolutional neural networks can learn discriminative spatial features, which play a paramount role in HSI interpretation. However, most of these methods ignore the distinctive spectral-spatial characteristic of hyperspectral data. In addition, a large amount of unlabeled data remains an unexploited gold mine for efficient data use. Therefore, we proposed an integration of generative adversarial networks (GANs) and probabilistic graphical models for HSI classification. Specifically, we used a spectral-spatial generator and a discriminator to identify land cover categories of hyperspectral cubes. Moreover, to take advantage of a large amount of unlabeled data, we adopted a conditional random field to refine the preliminary classification results generated by GANs. Experimental results obtained using two commonly studied datasets demonstrate that the proposed framework achieved encouraging classification accuracy using a small number of data for training.
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