Model agnostic local variable importance for locally dependent relationships

Global variable importance measures are commonly used to interpret machine learning model results. Local variable importance techniques assess how variables contribute to individual observations rather than the entire dataset. Current methods typically fail to accurately reflect locally dependent relationships between variables and instead focus on marginal importance values. Additionally, they are not natively adapted for multi-class classification problems. We propose a new model-agnostic method for calculating local variable importance, CLIQUE, that captures locally dependent relationships, contains improvements over permutation-based methods, and can be directly applied to multi-class classification problems. Simulated and real-world examples show that CLIQUE emphasizes locally dependent information and properly reduces bias in regions where variables do not affect the response.

Forest Proximities for Time Series

RF-GAP has recently been introduced as an improved random forest proximity measure. In this paper, we present PF-GAP, an extension of RF-GAP proximities to proximity forests, an accurate and efficient time series classification model. We use the forest proximities in connection with Multi-Dimensional Scaling to obtain vector embeddings of univariate time series, comparing the embeddings to those obtained using various time series distance measures. We also use the forest proximities alongside Local Outlier Factors to investigate the connection between misclassified points and outliers, comparing with nearest neighbor classifiers which use time series distance measures. We show that the forest proximities may exhibit a stronger connection between misclassified points and outliers than nearest neighbor classifiers.

Training-Free Guidance for Discrete Diffusion Models for Molecular Generation

Training-free guidance methods for continuous data have seen an explosion of interest due to the fact that they enable foundation diffusion models to be paired with interchangable guidance models. Currently, equivalent guidance methods for discrete diffusion models are unknown. We present a framework for applying training-free guidance to discrete data and demonstrate its utility on molecular graph generation tasks using the discrete diffusion model architecture of DiGress. We pair this model with guidance functions that return the proportion of heavy atoms that are a specific atom type and the molecular weight of the heavy atoms and demonstrate our method's ability to guide the data generation.

Enhancing Supervised Visualization through Autoencoder and Random Forest Proximities for Out-of-Sample Extension

The value of supervised dimensionality reduction lies in its ability to uncover meaningful connections between data features and labels. Common dimensionality reduction methods embed a set of fixed, latent points, but are not capable of generalizing to an unseen test set. In this paper, we provide an out-of-sample extension method for the random forest-based supervised dimensionality reduction method, RF-PHATE, combining information learned from the random forest model with the function-learning capabilities of autoencoders. Through quantitative assessment of various autoencoder architectures, we identify that networks that reconstruct random forest proximities are more robust for the embedding extension problem. Furthermore, by leveraging proximity-based prototypes, we achieve a 40% reduction in training time without compromising extension quality. Our method does not require label information for out-of-sample points, thus serving as a semi-supervised method, and can achieve consistent quality using only 10% of the training data.

Symmetry Discovery Beyond Affine Transformations

Symmetry detection has been shown to improve various machine learning tasks. In the context of continuous symmetry detection, current state of the art experiments are limited to the detection of affine transformations. Under the manifold assumption, we outline a framework for discovering continuous symmetry in data beyond the affine transformation group. We also provide a similar framework for discovering discrete symmetry. We experimentally compare our method to an existing method known as LieGAN and show that our method is competitive at detecting affine symmetries for large sample sizes and superior than LieGAN for small sample sizes. We also show our method is able to detect continuous symmetries beyond the affine group and is generally more computationally efficient than LieGAN.

Noisy Data Visualization using Functional Data Analysis

Data visualization via dimensionality reduction is an important tool in exploratory data analysis. However, when the data are noisy, many existing methods fail to capture the underlying structure of the data. The method called Empirical Intrinsic Geometry (EIG) was previously proposed for performing dimensionality reduction on high dimensional dynamical processes while theoretically eliminating all noise. However, implementing EIG in practice requires the construction of high-dimensional histograms, which suffer from the curse of dimensionality. Here we propose a new data visualization method called Functional Information Geometry (FIG) for dynamical processes that adapts the EIG framework while using approaches from functional data analysis to mitigate the curse of dimensionality. We experimentally demonstrate that the resulting method outperforms a variant of EIG designed for visualization in terms of capturing the true structure, hyperparameter robustness, and computational speed. We then use our method to visualize EEG brain measurements of sleep activity.

Local Background Estimation for Improved Gas Plume Identification in Hyperspectral Images

Deep learning identification models have shown promise for identifying gas plumes in Longwave IR hyperspectral images of urban scenes, particularly when a large library of gases are being considered. Because many gases have similar spectral signatures, it is important to properly estimate the signal from a detected plume. Typically, a scene's global mean spectrum and covariance matrix are estimated to whiten the plume's signal, which removes the background's signature from the gas signature. However, urban scenes can have many different background materials that are spatially and spectrally heterogeneous. This can lead to poor identification performance when the global background estimate is not representative of a given local background material. We use image segmentation, along with an iterative background estimation algorithm, to create local estimates for the various background materials that reside underneath a gas plume. Our method outperforms global background estimation on a set of simulated and real gas plumes. This method shows promise in increasing deep learning identification confidence, while being simple and easy to tune when considering diverse plumes.

Manifold Alignment with Label Information

Multi-domain data is becoming increasingly common and presents both challenges and opportunities in the data science community. The integration of distinct data-views can be used for exploratory data analysis, and benefit downstream analysis including machine learning related tasks. With this in mind, we present a novel manifold alignment method called MALI (Manifold alignment with label information) that learns a correspondence between two distinct domains. MALI can be considered as belonging to a middle ground between the more commonly addressed semi-supervised manifold alignment problem with some known correspondences between the two domains, and the purely unsupervised case, where no known correspondences are provided. To do this, MALI learns the manifold structure in both domains via a diffusion process and then leverages discrete class labels to guide the alignment. By aligning two distinct domains, MALI recovers a pairing and a common representation that reveals related samples in both domains. Additionally, MALI can be used for the transfer learning problem known as domain adaptation. We show that MALI outperforms the current state-of-the-art manifold alignment methods across multiple datasets.

Diffusion Transport Alignment

The integration of multimodal data presents a challenge in cases when the study of a given phenomena by different instruments or conditions generates distinct but related domains. Many existing data integration methods assume a known one-to-one correspondence between domains of the entire dataset, which may be unrealistic. Furthermore, existing manifold alignment methods are not suited for cases where the data contains domain-specific regions, i.e., there is not a counterpart for a certain portion of the data in the other domain. We propose Diffusion Transport Alignment (DTA), a semi-supervised manifold alignment method that exploits prior correspondence knowledge between only a few points to align the domains. By building a diffusion process, DTA finds a transportation plan between data measured from two heterogeneous domains with different feature spaces, which by assumption, share a similar geometrical structure coming from the same underlying data generating process. DTA can also compute a partial alignment in a data-driven fashion, resulting in accurate alignments when some data are measured in only one domain. We empirically demonstrate that DTA outperforms other methods in aligning multimodal data in this semisupervised setting. We also empirically show that the alignment obtained by DTA can improve the performance of machine learning tasks, such as domain adaptation, inter-domain feature mapping, and exploratory data analysis, while outperforming competing methods.

Geometry- and Accuracy-Preserving Random Forest Proximities

Random forests are considered one of the best out-of-the-box classification and regression algorithms due to their high level of predictive performance with relatively little tuning. Pairwise proximities can be computed from a trained random forest which measure the similarity between data points relative to the supervised task. Random forest proximities have been used in many applications including the identification of variable importance, data imputation, outlier detection, and data visualization. However, existing definitions of random forest proximities do not accurately reflect the data geometry learned by the random forest. In this paper, we introduce a novel definition of random forest proximities called Random Forest-Geometry- and Accuracy-Preserving proximities (RF-GAP). We prove that the proximity-weighted sum (regression) or majority vote (classification) using RF-GAP exactly match the out-of-bag random forest prediction, thus capturing the data geometry learned by the random forest. We empirically show that this improved geometric representation outperforms traditional random forest proximities in tasks such as data imputation and provides outlier detection and visualization results consistent with the learned data geometry.