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An Empirical Bayes Approach to Optimizing Machine Learning Algorithms

Neural Information Processing Systems

There is rapidly growing interest in using Bayesian optimization to tune model and inference hyperparameters for machine learning algorithms that take a long time to run. For example, Spearmint is a popular software package for selecting the optimal number of layers and learning rate in neural networks. But given that there is uncertainty about which hyperparameters give the best predictive performance, and given that fitting a model for each choice of hyperparameters is costly, it is arguably wasteful to throw away all but the best result, as per Bayesian optimization. A related issue is the danger of overfitting the validation data when optimizing many hyperparameters. In this paper, we consider an alternative approach that uses more samples from the hyperparameter selection procedure to average over the uncertainty in model hyperparameters. The resulting approach, empirical Bayes for hyperparameter averaging (EB-Hyp) predicts held-out data better than Bayesian optimization in two experiments on latent Dirichlet allocation and deep latent Gaussian models. EB-Hyp suggests a simpler approach to evaluating and deploying machine learning algorithms that does not require a separate validation data set and hyperparameter selection procedure.


Regularization Learning Networks: Deep Learning for Tabular Datasets

Neural Information Processing Systems

Despite their impressive performance, Deep Neural Networks (DNNs) typically underperform Gradient Boosting Trees (GBTs) on many tabular-dataset learning tasks. We propose that applying a different regularization coefficient to each weight might boost the performance of DNNs by allowing them to make more use of the more relevant inputs. However, this will lead to an intractable number of hyperparameters. Here, we introduce Regularization Learning Networks (RLNs), which overcome this challenge by introducing an efficient hyperparameter tuning scheme which minimizes a new Counterfactual Loss. Our results show that RLNs significantly improve DNNs on tabular datasets, and achieve comparable results to GBTs, with the best performance achieved with an ensemble that combines GBTs and RLNs. RLNs produce extremely sparse networks, eliminating up to 99.8% of the network edges and 82% of the input features, thus providing more interpretable models and reveal the importance that the network assigns to different inputs. RLNs could efficiently learn a single network in datasets that comprise both tabular and unstructured data, such as in the setting of medical imaging accompanied by electronic health records.


Learning filter widths of spectral decompositions with wavelets

Neural Information Processing Systems

Time series classification using deep neural networks, such as convolutional neural networks (CNN), operate on the spectral decomposition of the time series computed using a preprocessing step. This step can include a large number of hyperparameters, such as window length, filter widths, and filter shapes, each with a range of possible values that must be chosen using time and data intensive cross-validation procedures. We propose the wavelet deconvolution (WD) layer as an efficient alternative to this preprocessing step that eliminates a significant number of hyperparameters. The WD layer uses wavelet functions with adjustable scale parameters to learn the spectral decomposition directly from the signal. Using backpropagation, we show the scale parameters can be optimized with gradient descent. Furthermore, the WD layer adds interpretability to the learned time series classifier by exploiting the properties of the wavelet transform.


Towards a data-scale independent regulariser for robust sparse identification of non-linear dynamics

Raut, Jay, Wilke, Daniel N., Schmidt, Stephan

arXiv.org Machine Learning

Data normalisation, a common and often necessary preprocessing step in engineering and scientific applications, can severely distort the discovery of governing equations by magnitudebased sparse regression methods. This issue is particularly acute for the Sparse Identification of Nonlinear Dynamics (SINDy) framework, where the core assumption of sparsity is undermined by the interaction between data scaling and measurement noise. The resulting discovered models can be dense, uninterpretable, and physically incorrect. To address this critical vulnerability, we introduce the Sequential Thresholding of Coefficient of Variation (STCV), a novel, computationally efficient sparse regression algorithm that is inherently robust to data scaling. STCV replaces conventional magnitude-based thresholding with a dimensionless statistical metric, the Coefficient Presence (CP), which assesses the statistical validity and consistency of candidate terms in the model library. This shift from magnitude to statistical significance makes the discovery process invariant to arbitrary data scaling. Through comprehensive benchmarking on canonical dynamical systems and practical engineering problems, including a physical mass-spring-damper experiment, we demonstrate that STCV consistently and significantly outperforms standard Sequential Thresholding Least Squares (STLSQ) and Ensemble-SINDy (E-SINDy) on normalised, noisy datasets. The results show that STCV-based methods can successfully identify the correct, sparse physical laws even when other methods fail. By mitigating the distorting effects of normalisation, STCV makes sparse system identification a more reliable and automated tool for real-world applications, thereby enhancing model interpretability and trustworthiness.






ed519dacc89b2bead3f453b0b05a4a8b-Supplemental.pdf

Neural Information Processing Systems

Figure 11: Comparison of HCAM (labeled as HTM) with different chunk sizes to TrXL across the different ballet levels. The performance of the HCAM model is robust to varying chunk size, indicating that HCAM does not need a task-relevant segmentation to perform well.