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Diane Oyen

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Published work

10 published item(s)

preprint2026arXiv

HyCOP: Hybrid Composition Operators for Interpretable Learning of PDEs

We introduce HyCOP, a modular framework that learns parametric PDE solution operators by composing simple modules (advection, diffusion, learned closures, boundary handling) in a query-conditioned way. Rather than learning a monolithic map, HyCOP learns a policy over short programs - which module to apply and for how long - conditioned on regime features and state statistics. Modules may be numerical sub-solvers or learned components, enabling hybrid surrogates evaluated at arbitrary query times without autoregressive rollout. Across diverse PDE benchmarks, HyCOP produces interpretable programs, delivers order-of-magnitude OOD improvements over monolithic neural operators, and supports modular transfer through dictionary updates (e.g., boundary swaps, residual enrichment). Our theory characterizes expressivity and gives an error decomposition that separates composition error from module error and doubles as a process-level diagnostic.

preprint2023arXiv

SpectroscopyNet: Learning to pre-process Spectroscopy Signals without clean data

In this work we propose a deep learning approach to clean spectroscopy signals using only uncleaned data. Cleaning signals from spectroscopy instrument noise is challenging as noise exhibits an unknown, non-zero mean, multivariate distributions. Our framework is a siamese neural net that learns identifiable disentanglement of the signal and noise components under a stationarity assumption. The disentangled representations satisfy reconstruction fidelity, reduce consistencies with measurements of unrelated targets and imposes relaxed-orthogonality constraints between the signal and noise representations. Evaluations on a laser induced breakdown spectroscopy (LIBS) dataset from the ChemCam instrument onboard the Martian Curiosity rover show a superior performance in cleaning LIBS measurements compared to the standard feature engineered approaches being used by the ChemCam team.

preprint2022arXiv

Robustness to Label Noise Depends on the Shape of the Noise Distribution in Feature Space

Machine learning classifiers have been demonstrated, both empirically and theoretically, to be robust to label noise under certain conditions -- notably the typical assumption is that label noise is independent of the features given the class label. We provide a theoretical framework that generalizes beyond this typical assumption by modeling label noise as a distribution over feature space. We show that both the scale and the shape of the noise distribution influence the posterior likelihood; and the shape of the noise distribution has a stronger impact on classification performance if the noise is concentrated in feature space where the decision boundary can be moved. For the special case of uniform label noise (independent of features and the class label), we show that the Bayes optimal classifier for $c$ classes is robust to label noise until the ratio of noisy samples goes above $\frac{c-1}{c}$ (e.g. 90% for 10 classes), which we call the tipping point. However, for the special case of class-dependent label noise (independent of features given the class label), the tipping point can be as low as 50%. Most importantly, we show that when the noise distribution targets decision boundaries (label noise is directly dependent on feature space), classification robustness can drop off even at a small scale of noise. Even when evaluating recent label-noise mitigation methods we see reduced accuracy when label noise is dependent on features. These findings explain why machine learning often handles label noise well if the noise distribution is uniform in feature-space; yet it also points to the difficulty of overcoming label noise when it is concentrated in a region of feature space where a decision boundary can move.

preprint2020arXiv

Deep Spectral CNN for Laser Induced Breakdown Spectroscopy

This work proposes a spectral convolutional neural network (CNN) operating on laser induced breakdown spectroscopy (LIBS) signals to learn to (1) disentangle spectral signals from the sources of sensor uncertainty (i.e., pre-process) and (2) get qualitative and quantitative measures of chemical content of a sample given a spectral signal (i.e., calibrate). Once the spectral CNN is trained, it can accomplish either task through a single feed-forward pass, with real-time benefits and without any additional side information requirements including dark current, system response, temperature and detector-to-target range. Our experiments demonstrate that the proposed method outperforms the existing approaches used by the Mars Science Lab for pre-processing and calibration for remote sensing observations from the Mars rover, 'Curiosity'.

preprint2020arXiv

Diagram Image Retrieval using Sketch-Based Deep Learning and Transfer Learning

Resolution of the complex problem of image retrieval for diagram images has yet to be reached. Deep learning methods continue to excel in the fields of object detection and image classification applied to natural imagery. However, the application of such methodologies applied to binary imagery remains limited due to lack of crucial features such as textures,color and intensity information. This paper presents a deep learning based method for image-based search for binary patent images by taking advantage of existing large natural image repositories for image search and sketch-based methods (Sketches are not identical to diagrams, but they do share some characteristics; for example, both imagery types are gray scale (binary), composed of contours, and are lacking in texture). We begin by using deep learning to generate sketches from natural images for image retrieval and then train a second deep learning model on the sketches. We then use our small set of manually labeled patent diagram images via transfer learning to adapt the image search from sketches of natural images to diagrams. Our experiment results show the effectiveness of deep learning with transfer learning for detecting near-identical copies in patent images and querying similar images based on content.

preprint2020arXiv

Learning Spatial Relationships between Samples of Patent Image Shapes

Binary image based classification and retrieval of documents of an intellectual nature is a very challenging problem. Variations in the binary image generation mechanisms which are subject to the document artisan designer including drawing style, view-point, inclusion of multiple image components are plausible causes for increasing the complexity of the problem. In this work, we propose a method suitable to binary images which bridges some of the successes of deep learning (DL) to alleviate the problems introduced by the aforementioned variations. The method consists on extracting the shape of interest from the binary image and applying a non-Euclidean geometric neural-net architecture to learn the local and global spatial relationships of the shape. Empirical results show that our method is in some sense invariant to the image generation mechanism variations and achieves results outperforming existing methods in a patent image dataset benchmark.

preprint2020arXiv

TGGLines: A Robust Topological Graph Guided Line Segment Detector for Low Quality Binary Images

Line segment detection is an essential task in computer vision and image analysis, as it is the critical foundation for advanced tasks such as shape modeling and road lane line detection for autonomous driving. We present a robust topological graph guided approach for line segment detection in low quality binary images (hence, we call it TGGLines). Due to the graph-guided approach, TGGLines not only detects line segments, but also organizes the segments with a line segment connectivity graph, which means the topological relationships (e.g., intersection, an isolated line segment) of the detected line segments are captured and stored; whereas other line detectors only retain a collection of loose line segments. Our empirical results show that the TGGLines detector visually and quantitatively outperforms state-of-the-art line segment detection methods. In addition, our TGGLines approach has the following two competitive advantages: (1) our method only requires one parameter and it is adaptive, whereas almost all other line segment detection methods require multiple (non-adaptive) parameters, and (2) the line segments detected by TGGLines are organized by a line segment connectivity graph.

preprint2015arXiv

Learning Planar Ising Models

Inference and learning of graphical models are both well-studied problems in statistics and machine learning that have found many applications in science and engineering. However, exact inference is intractable in general graphical models, which suggests the problem of seeking the best approximation to a collection of random variables within some tractable family of graphical models. In this paper, we focus on the class of planar Ising models, for which exact inference is tractable using techniques of statistical physics. Based on these techniques and recent methods for planarity testing and planar embedding, we propose a simple greedy algorithm for learning the best planar Ising model to approximate an arbitrary collection of binary random variables (possibly from sample data). Given the set of all pairwise correlations among variables, we select a planar graph and optimal planar Ising model defined on this graph to best approximate that set of correlations. We demonstrate our method in simulations and for the application of modeling senate voting records.

preprint2013arXiv

Bayesian Discovery of Multiple Bayesian Networks via Transfer Learning

Bayesian network structure learning algorithms with limited data are being used in domains such as systems biology and neuroscience to gain insight into the underlying processes that produce observed data. Learning reliable networks from limited data is difficult, therefore transfer learning can improve the robustness of learned networks by leveraging data from related tasks. Existing transfer learning algorithms for Bayesian network structure learning give a single maximum a posteriori estimate of network models. Yet, many other models may be equally likely, and so a more informative result is provided by Bayesian structure discovery. Bayesian structure discovery algorithms estimate posterior probabilities of structural features, such as edges. We present transfer learning for Bayesian structure discovery which allows us to explore the shared and unique structural features among related tasks. Efficient computation requires that our transfer learning objective factors into local calculations, which we prove is given by a broad class of transfer biases. Theoretically, we show the efficiency of our approach. Empirically, we show that compared to single task learning, transfer learning is better able to positively identify true edges. We apply the method to whole-brain neuroimaging data.

preprint2013arXiv

Controlling the Precision-Recall Tradeoff in Differential Dependency Network Analysis

Graphical models have gained a lot of attention recently as a tool for learning and representing dependencies among variables in multivariate data. Often, domain scientists are looking specifically for differences among the dependency networks of different conditions or populations (e.g. differences between regulatory networks of different species, or differences between dependency networks of diseased versus healthy populations). The standard method for finding these differences is to learn the dependency networks for each condition independently and compare them. We show that this approach is prone to high false discovery rates (low precision) that can render the analysis useless. We then show that by imposing a bias towards learning similar dependency networks for each condition the false discovery rates can be reduced to acceptable levels, at the cost of finding a reduced number of differences. Algorithms developed in the transfer learning literature can be used to vary the strength of the imposed similarity bias and provide a natural mechanism to smoothly adjust this differential precision-recall tradeoff to cater to the requirements of the analysis conducted. We present real case studies (oncological and neurological) where domain experts use the proposed technique to extract useful differential networks that shed light on the biological processes involved in cancer and brain function.