Surrogate kernel-based methods offer a flexible solution to structured output prediction by leveraging the kernel trick in both input and output spaces. In contrast to energy-based models, they avoid to pay the cost of inference during training, while enjoying statistical guarantees. However, without approximation, these approaches are condemned to be used only on a limited amount of training data. In this paper, we propose to equip surrogate kernel methods with approximations based on sketching, seen as low rank projections of feature maps both on input and output feature maps. We showcase the approach on Input Output Kernel ridge Regression (or Kernel Dependency Estimation) and provide excess risk bounds that can be in turn directly plugged on the final predictive model. An analysis of the complexity in time and memory show that sketching the input kernel mostly reduces training time while sketching the output kernel allows to reduce the inference time. Furthermore, we show that Gaussian and sub-Gaussian sketches are admissible sketches in the sense that they induce projection operators ensuring a small excess risk. Experiments on different tasks consolidate our findings.
相關內容
Given their adaptability and encouraging performance, deep-learning models are becoming standard for motion prediction in autonomous driving. However, with great flexibility comes a lack of interpretability and possible violations of physical constraints. Accompanying these data-driven methods with differentially-constrained motion models to provide physically feasible trajectories is a promising future direction. The foundation for this work is a previously introduced graph-neural-network-based model, MTP-GO. The neural network learns to compute the inputs to an underlying motion model to provide physically feasible trajectories. This research investigates the performance of various motion models in combination with numerical solvers for the prediction task. The study shows that simpler models, such as low-order integrator models, are preferred over more complex ones, e.g., kinematic models, to achieve accurate predictions. Further, the numerical solver can have a substantial impact on performance, advising against commonly used first-order methods like Euler forward. Instead, a second-order method like Heun's can significantly improve predictions.
Local feature matching is challenging due to textureless and repetitive patterns. Existing methods focus on using appearance features and global interaction and matching, while the importance of geometry priors in local feature matching has not been fully exploited. Different from these methods, in this paper, we delve into the importance of geometry prior and propose Structured Epipolar Matcher (SEM) for local feature matching, which can leverage the geometric information in an iterative matching way. The proposed model enjoys several merits. First, our proposed Structured Feature Extractor can model the relative positional relationship between pixels and high-confidence anchor points. Second, our proposed Epipolar Attention and Matching can filter out irrelevant areas by utilizing the epipolar constraint. Extensive experimental results on five standard benchmarks demonstrate the superior performance of our SEM compared to state-of-the-art methods. Project page: //sem2023.github.io.
A predictive model makes outcome predictions based on some given features, i.e., it estimates the conditional probability of the outcome given a feature vector. In general, a predictive model cannot estimate the causal effect of a feature on the outcome, i.e., how the outcome will change if the feature is changed while keeping the values of other features unchanged. This is because causal effect estimation requires interventional probabilities. However, many real world problems such as personalised decision making, recommendation, and fairness computing, need to know the causal effect of any feature on the outcome for a given instance. This is different from the traditional causal effect estimation problem with a fixed treatment variable. This paper first tackles the challenge of estimating the causal effect of any feature (as the treatment) on the outcome w.r.t. a given instance. The theoretical results naturally link a predictive model to causal effect estimations and imply that a predictive model is causally interpretable when the conditions identified in the paper are satisfied. The paper also reveals the robust property of a causally interpretable model. We use experiments to demonstrate that various types of predictive models, when satisfying the conditions identified in this paper, can estimate the causal effects of features as accurately as state-of-the-art causal effect estimation methods. We also show the potential of such causally interpretable predictive models for robust predictions and personalised decision making.
This paper proposes a hybrid synthesis method for multi-exposure image fusion taken by hand-held cameras. Motions either due to the shaky camera or caused by dynamic scenes should be compensated before any content fusion. Any misalignment can easily cause blurring/ghosting artifacts in the fused result. Our hybrid method can deal with such motions and maintain the exposure information of each input effectively. In particular, the proposed method first applies optical flow for a coarse registration, which performs well with complex non-rigid motion but produces deformations at regions with missing correspondences. The absence of correspondences is due to the occlusions of scene parallax or the moving contents. To correct such error registration, we segment images into superpixels and identify problematic alignments based on each superpixel, which is further aligned by PatchMatch. The method combines the efficiency of optical flow and the accuracy of PatchMatch. After PatchMatch correction, we obtain a fully aligned image stack that facilitates a high-quality fusion that is free from blurring/ghosting artifacts. We compare our method with existing fusion algorithms on various challenging examples, including the static/dynamic, the indoor/outdoor and the daytime/nighttime scenes. Experiment results demonstrate the effectiveness and robustness of our method.
With the rising complexity of numerous novel applications that serve our modern society comes the strong need to design efficient computing platforms. Designing efficient hardware is, however, a complex multi-objective problem that deals with multiple parameters and their interactions. Given that there are a large number of parameters and objectives involved in hardware design, synthesizing all possible combinations is not a feasible method to find the optimal solution. One promising approach to tackle this problem is statistical modeling of a desired hardware performance. Here, we propose a model-based active learning approach to solve this problem. Our proposed method uses Bayesian models to characterize various aspects of hardware performance. We also use transfer learning and Gaussian regression bootstrapping techniques in conjunction with active learning to create more accurate models. Our proposed statistical modeling method provides hardware models that are sufficiently accurate to perform design space exploration as well as performance prediction simultaneously. We use our proposed method to perform design space exploration and performance prediction for various hardware setups, such as micro-architecture design and OpenCL kernels for FPGA targets. Our experiments show that the number of samples required to create performance models significantly reduces while maintaining the predictive power of our proposed statistical models. For instance, in our performance prediction setting, the proposed method needs 65% fewer samples to create the model, and in the design space exploration setting, our proposed method can find the best parameter settings by exploring less than 50 samples.
To estimate causal effects, analysts performing observational studies in health settings utilize several strategies to mitigate bias due to confounding by indication. There are two broad classes of approaches for these purposes: use of confounders and instrumental variables (IVs). Because such approaches are largely characterized by untestable assumptions, analysts must operate under an indefinite paradigm that these methods will work imperfectly. In this tutorial, we formalize a set of general principles and heuristics for estimating causal effects in the two approaches when the assumptions are potentially violated. This crucially requires reframing the process of observational studies as hypothesizing potential scenarios where the estimates from one approach are less inconsistent than the other. While most of our discussion of methodology centers around the linear setting, we touch upon complexities in non-linear settings and flexible procedures such as target minimum loss-based estimation (TMLE) and double machine learning (DML). To demonstrate the application of our principles, we investigate the use of donepezil off-label for mild cognitive impairment (MCI). We compare and contrast results from confounder and IV methods, traditional and flexible, within our analysis and to a similar observational study and clinical trial.
We introduce the Weak-form Estimation of Nonlinear Dynamics (WENDy) method for estimating model parameters for non-linear systems of ODEs. Without relying on any numerical differential equation solvers, WENDy computes accurate estimates and is robust to large (biologically relevant) levels of measurement noise. For low dimensional systems with modest amounts of data, WENDy is competitive with conventional forward solver-based nonlinear least squares methods in terms of speed and accuracy. For both higher dimensional systems and stiff systems, WENDy is typically both faster (often by orders of magnitude) and more accurate than forward solver-based approaches. The core mathematical idea involves an efficient conversion of the strong form representation of a model to its weak form, and then solving a regression problem to perform parameter inference. The core statistical idea rests on the Errors-In-Variables framework, which necessitates the use of the iteratively reweighted least squares algorithm. Further improvements are obtained by using orthonormal test functions, created from a set of C-infinity bump functions of varying support sizes. We demonstrate the high robustness and computational efficiency by applying WENDy to estimate parameters in some common models from population biology, neuroscience, and biochemistry, including logistic growth, Lotka-Volterra, FitzHugh-Nagumo, Hindmarsh-Rose, and a Protein Transduction Benchmark model. Software and code for reproducing the examples is available at (//github.com/MathBioCU/WENDy).
Range aggregate queries (RAQs) are an integral part of many real-world applications, where, often, fast and approximate answers for the queries are desired. Recent work has studied answering RAQs using machine learning (ML) models, where a model of the data is learned to answer the queries. However, there is no theoretical understanding of why and when the ML based approaches perform well. Furthermore, since the ML approaches model the data, they fail to capitalize on any query specific information to improve performance in practice. In this paper, we focus on modeling ``queries'' rather than data and train neural networks to learn the query answers. This change of focus allows us to theoretically study our ML approach to provide a distribution and query dependent error bound for neural networks when answering RAQs. We confirm our theoretical results by developing NeuroSketch, a neural network framework to answer RAQs in practice. Extensive experimental study on real-world, TPC-benchmark and synthetic datasets show that NeuroSketch answers RAQs multiple orders of magnitude faster than state-of-the-art and with better accuracy.
Traditional methods for link prediction can be categorized into three main types: graph structure feature-based, latent feature-based, and explicit feature-based. Graph structure feature methods leverage some handcrafted node proximity scores, e.g., common neighbors, to estimate the likelihood of links. Latent feature methods rely on factorizing networks' matrix representations to learn an embedding for each node. Explicit feature methods train a machine learning model on two nodes' explicit attributes. Each of the three types of methods has its unique merits. In this paper, we propose SEAL (learning from Subgraphs, Embeddings, and Attributes for Link prediction), a new framework for link prediction which combines the power of all the three types into a single graph neural network (GNN). GNN is a new type of neural network which directly accepts graphs as input and outputs their labels. In SEAL, the input to the GNN is a local subgraph around each target link. We prove theoretically that our local subgraphs also reserve a great deal of high-order graph structure features related to link existence. Another key feature is that our GNN can naturally incorporate latent features and explicit features. It is achieved by concatenating node embeddings (latent features) and node attributes (explicit features) in the node information matrix for each subgraph, thus combining the three types of features to enhance GNN learning. Through extensive experiments, SEAL shows unprecedentedly strong performance against a wide range of baseline methods, including various link prediction heuristics and network embedding methods.
Dynamic programming (DP) solves a variety of structured combinatorial problems by iteratively breaking them down into smaller subproblems. In spite of their versatility, DP algorithms are usually non-differentiable, which hampers their use as a layer in neural networks trained by backpropagation. To address this issue, we propose to smooth the max operator in the dynamic programming recursion, using a strongly convex regularizer. This allows to relax both the optimal value and solution of the original combinatorial problem, and turns a broad class of DP algorithms into differentiable operators. Theoretically, we provide a new probabilistic perspective on backpropagating through these DP operators, and relate them to inference in graphical models. We derive two particular instantiations of our framework, a smoothed Viterbi algorithm for sequence prediction and a smoothed DTW algorithm for time-series alignment. We showcase these instantiations on two structured prediction tasks and on structured and sparse attention for neural machine translation.
小貼士
登錄享
相關主題
注冊地址： 北京市海淀區羊坊店路18號2幢3層301-191