Feature selection is a technique in statistical prediction modeling that identifies features in a record with a strong statistical connection to the target variable. Excluding features with a weak statistical connection to the target variable in training not only drops the dimension of the data, which decreases the time complexity of the algorithm, it also decreases noise within the data which assists in avoiding overfitting. In all, feature selection assists in training a robust statistical model that performs well and is stable. Given the lack of scalability in classical computation, current techniques only consider the predictive power of the feature and not redundancy between the features themselves. Recent advancements in feature selection that leverages quantum annealing (QA) gives a scalable technique that aims to maximize the predictive power of the features while minimizing redundancy. As a consequence, it is expected that this algorithm would assist in the bias/variance trade-off yielding better features for training a statistical model. This paper tests this intuition against classical methods by utilizing open-source data sets and evaluate the efficacy of each trained statistical model well-known prediction algorithms. The numerical results display an advantage utilizing the features selected from the algorithm that leveraged QA.
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This work introduces a reduced order modeling (ROM) framework for the solution of parameterized second-order linear elliptic partial differential equations formulated on unfitted geometries. The goal is to construct efficient projection-based ROMs, which rely on techniques such as the reduced basis method and discrete empirical interpolation. The presence of geometrical parameters in unfitted domain discretizations entails challenges for the application of standard ROMs. Therefore, in this work we propose a methodology based on i) extension of snapshots on the background mesh and ii) localization strategies to decrease the number of reduced basis functions. The method we obtain is computationally efficient and accurate, while it is agnostic with respect to the underlying discretization choice. We test the applicability of the proposed framework with numerical experiments on two model problems, namely the Poisson and linear elasticity problems. In particular, we study several benchmarks formulated on two-dimensional, trimmed domains discretized with splines and we observe a significant reduction of the online computational cost compared to standard ROMs for the same level of accuracy. Moreover, we show the applicability of our methodology to a three-dimensional geometry of a linear elastic problem.
Backpropagation algorithm has been widely used as a mainstream learning procedure for neural networks in the past decade, and has played a significant role in the development of deep learning. However, there exist some limitations associated with this algorithm, such as getting stuck in local minima and experiencing vanishing/exploding gradients, which have led to questions about its biological plausibility. To address these limitations, alternative algorithms to backpropagation have been preliminarily explored, with the Forward-Forward (FF) algorithm being one of the most well-known. In this paper we propose a new learning framework for neural networks, namely Cascaded Forward (CaFo) algorithm, which does not rely on BP optimization as that in FF. Unlike FF, our framework directly outputs label distributions at each cascaded block, which does not require generation of additional negative samples and thus leads to a more efficient process at both training and testing. Moreover, in our framework each block can be trained independently, so it can be easily deployed into parallel acceleration systems. The proposed method is evaluated on four public image classification benchmarks, and the experimental results illustrate significant improvement in prediction accuracy in comparison with the baseline.
Quantum annealing is a specialized type of quantum computation that aims to use quantum fluctuations in order to obtain global minimum solutions of combinatorial optimization problems. D-Wave Systems, Inc., manufactures quantum annealers, which are available as cloud computing resources, and allow users to program the anneal schedules used in the annealing computation. In this paper, we are interested in improving the quality of the solutions returned by a quantum annealer by encoding an initial state. We explore two D-Wave features allowing one to encode such an initial state: the reverse annealing and the h-gain features. Reverse annealing (RA) aims to refine a known solution following an anneal path starting with a classical state representing a good solution, going backwards to a point where a transverse field is present, and then finishing the annealing process with a forward anneal. The h-gain (HG) feature allows one to put a time-dependent weighting scheme on linear ($h$) biases of the Hamiltonian, and we demonstrate that this feature likewise can be used to bias the annealing to start from an initial state. We also consider a hybrid method consisting of a backward phase resembling RA, and a forward phase using the HG initial state encoding. Importantly, we investigate the idea of iteratively applying RA and HG to a problem, with the goal of monotonically improving on an initial state that is not optimal. The HG encoding technique is evaluated on a variety of input problems including the weighted Maximum Cut problem and the weighted Maximum Clique problem, demonstrating that the HG technique is a viable alternative to RA for some problems. We also investigate how the iterative procedures perform for both RA and HG initial state encoding on random spin glasses with the native connectivity of the D-Wave Chimera and Pegasus chips.
Generalization error predictors (GEPs) aim to predict model performance on unseen distributions by deriving dataset-level error estimates from sample-level scores. However, GEPs often utilize disparate mechanisms (e.g., regressors, thresholding functions, calibration datasets, etc), to derive such error estimates, which can obfuscate the benefits of a particular scoring function. Therefore, in this work, we rigorously study the effectiveness of popular scoring functions (confidence, local manifold smoothness, model agreement), independent of mechanism choice. We find, absent complex mechanisms, that state-of-the-art confidence- and smoothness- based scores fail to outperform simple model-agreement scores when estimating error under distribution shifts and corruptions. Furthermore, on realistic settings where the training data has been compromised (e.g., label noise, measurement noise, undersampling), we find that model-agreement scores continue to perform well and that ensemble diversity is important for improving its performance. Finally, to better understand the limitations of scoring functions, we demonstrate that simplicity bias, or the propensity of deep neural networks to rely upon simple but brittle features, can adversely affect GEP performance. Overall, our work carefully studies the effectiveness of popular scoring functions in realistic settings and helps to better understand their limitations.
The Internet has turned the entire world into a small village;this is because it has made it possible to share millions of images and videos. However, sending and receiving a huge amount of data is considered to be a main challenge. To address this issue, a new algorithm is required to reduce image bits and represent the data in a compressed form. Nevertheless, image compression is an important application for transferring large files and images. This requires appropriate and efficient transfers in this field to achieve the task and reach the best results. In this work, we propose a new algorithm based on discrete Hermite wavelets transformation (DHWT) that shows the efficiency and quality of the color images. By compressing the color image, this method analyzes it and divides it into approximate coefficients and detail coefficients after adding the wavelets into MATLAB. With Multi-Resolution Analyses (MRA), the appropriate filter is derived, and the mathematical aspects prove to be validated by testing a new filter and performing its operation. After the decomposition of the rows and upon the process of the reconstruction, taking the inverse of the filter and dealing with the columns of the matrix, the original matrix is improved by measuring the parameters of the image to achieve the best quality of the resulting image, such as the peak signal-to-noise ratio (PSNR), compression ratio (CR), bits per pixel (BPP), and mean square error (MSE).
Despite attractive theoretical guarantees and practical successes, Predictive Interval (PI) given by Conformal Prediction (CP) may not reflect the uncertainty of a given model. This limitation arises from CP methods using a constant correction for all test points, disregarding their individual uncertainties, to ensure coverage properties. To address this issue, we propose using a Quantile Regression Forest (QRF) to learn the distribution of nonconformity scores and utilizing the QRF's weights to assign more importance to samples with residuals similar to the test point. This approach results in PI lengths that are more aligned with the model's uncertainty. In addition, the weights learnt by the QRF provide a partition of the features space, allowing for more efficient computations and improved adaptiveness of the PI through groupwise conformalization. Our approach enjoys an assumption-free finite sample marginal and training-conditional coverage, and under suitable assumptions, it also ensures conditional coverage. Our methods work for any nonconformity score and are available as a Python package. We conduct experiments on simulated and real-world data that demonstrate significant improvements compared to existing methods.
A successful application of quantum annealing to machine learning is training restricted Boltzmann machines (RBM). However, many neural networks for vision applications are feedforward structures, such as multilayer perceptrons (MLP). Backpropagation is currently the most effective technique to train MLPs for supervised learning. This paper aims to be forward-looking by exploring the training of MLPs using quantum annealers. We exploit an equivalence between MLPs and energy-based models (EBM), which are a variation of RBMs with a maximum conditional likelihood objective. This leads to a strategy to train MLPs with quantum annealers as a sampling engine. We prove our setup for MLPs with sigmoid activation functions and one hidden layer, and demonstrated training of binary image classifiers on small subsets of the MNIST and Fashion-MNIST datasets using the D-Wave quantum annealer. Although problem sizes that are feasible on current annealers are limited, we obtained comprehensive results on feasible instances that validate our ideas. Our work establishes the potential of quantum computing for training MLPs.
Unsupervised domain adaptation has recently emerged as an effective paradigm for generalizing deep neural networks to new target domains. However, there is still enormous potential to be tapped to reach the fully supervised performance. In this paper, we present a novel active learning strategy to assist knowledge transfer in the target domain, dubbed active domain adaptation. We start from an observation that energy-based models exhibit free energy biases when training (source) and test (target) data come from different distributions. Inspired by this inherent mechanism, we empirically reveal that a simple yet efficient energy-based sampling strategy sheds light on selecting the most valuable target samples than existing approaches requiring particular architectures or computation of the distances. Our algorithm, Energy-based Active Domain Adaptation (EADA), queries groups of targe data that incorporate both domain characteristic and instance uncertainty into every selection round. Meanwhile, by aligning the free energy of target data compact around the source domain via a regularization term, domain gap can be implicitly diminished. Through extensive experiments, we show that EADA surpasses state-of-the-art methods on well-known challenging benchmarks with substantial improvements, making it a useful option in the open world. Code is available at //github.com/BIT-DA/EADA.
A key requirement for the success of supervised deep learning is a large labeled dataset - a condition that is difficult to meet in medical image analysis. Self-supervised learning (SSL) can help in this regard by providing a strategy to pre-train a neural network with unlabeled data, followed by fine-tuning for a downstream task with limited annotations. Contrastive learning, a particular variant of SSL, is a powerful technique for learning image-level representations. In this work, we propose strategies for extending the contrastive learning framework for segmentation of volumetric medical images in the semi-supervised setting with limited annotations, by leveraging domain-specific and problem-specific cues. Specifically, we propose (1) novel contrasting strategies that leverage structural similarity across volumetric medical images (domain-specific cue) and (2) a local version of the contrastive loss to learn distinctive representations of local regions that are useful for per-pixel segmentation (problem-specific cue). We carry out an extensive evaluation on three Magnetic Resonance Imaging (MRI) datasets. In the limited annotation setting, the proposed method yields substantial improvements compared to other self-supervision and semi-supervised learning techniques. When combined with a simple data augmentation technique, the proposed method reaches within 8% of benchmark performance using only two labeled MRI volumes for training, corresponding to only 4% (for ACDC) of the training data used to train the benchmark.
Transfer learning aims at improving the performance of target learners on target domains by transferring the knowledge contained in different but related source domains. In this way, the dependence on a large number of target domain data can be reduced for constructing target learners. Due to the wide application prospects, transfer learning has become a popular and promising area in machine learning. Although there are already some valuable and impressive surveys on transfer learning, these surveys introduce approaches in a relatively isolated way and lack the recent advances in transfer learning. As the rapid expansion of the transfer learning area, it is both necessary and challenging to comprehensively review the relevant studies. This survey attempts to connect and systematize the existing transfer learning researches, as well as to summarize and interpret the mechanisms and the strategies in a comprehensive way, which may help readers have a better understanding of the current research status and ideas. Different from previous surveys, this survey paper reviews over forty representative transfer learning approaches from the perspectives of data and model. The applications of transfer learning are also briefly introduced. In order to show the performance of different transfer learning models, twenty representative transfer learning models are used for experiments. The models are performed on three different datasets, i.e., Amazon Reviews, Reuters-21578, and Office-31. And the experimental results demonstrate the importance of selecting appropriate transfer learning models for different applications in practice.
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