Related papers: Principal Sensitivity Analysis
Multimodal sentiment analysis (MSA) is a research field that recognizes human sentiments by combining textual, visual, and audio modalities. The main challenge lies in integrating sentiment-related information from different modalities,…
Particle-based shape modeling (PSM) is a popular approach to automatically quantify shape variability in populations of anatomies. The PSM family of methods employs optimization to automatically populate a dense set of corresponding…
Latent state space models are a fundamental and widely used tool for modeling dynamical systems. However, they are difficult to learn from data and learned models often lack performance guarantees on inference tasks such as filtering and…
Big data is transforming our world, revolutionizing operations and analytics everywhere, from financial engineering to biomedical sciences. The complexity of big data often makes dimension reduction techniques necessary before conducting…
Interpretability is a critical factor in applying complex deep learning models to advance the understanding of brain disorders in neuroimaging studies. To interpret the decision process of a trained classifier, existing techniques typically…
Principal component analysis (PCA) is a widespread technique for data analysis that relies on the covariance-correlation matrix of the analyzed data. However to properly work with high-dimensional data, PCA poses severe mathematical…
We study attention mechanisms through the lens of a canonical unsupervised problem: principal component analysis (PCA). We show that, when trained on Gaussian data, both softmax and linear attention layers learn parameters that align with…
Principal Component Analysis (PCA) is a commonly used tool for dimension reduction and denoising. Therefore, it is also widely used on the data prior to training a neural network. However, this approach can complicate the explanation of…
Principal Component Analysis (PCA) is a dimension reduction technique. It produces inconsistent estimators when the dimensionality is moderate to high, which is often the problem in modern large-scale applications where algorithm…
We introduce a pruning algorithm that provably sparsifies the parameters of a trained model in a way that approximately preserves the model's predictive accuracy. Our algorithm uses a small batch of input points to construct a data-informed…
Principal component analysis (PCA) is a classical dimension reduction method which projects data onto the principal subspace spanned by the leading eigenvectors of the covariance matrix. However, it behaves poorly when the number of…
Recently, there has been much interest in deep learning techniques to do image compression and there have been claims that several of these produce better results than engineered compression schemes (such as JPEG, JPEG2000 or BPG). A…
Similarity measures are widely used to interpret the representational geometries used by neural networks to solve tasks. Yet, because existing methods compare the extrinsic geometry of representations in state space, rather than their…
Certain data are naturally modeled by networks or weighted graphs, be they arterial networks or mobility networks. When there is no canonical labeling of the nodes across the dataset, we talk about unlabeled networks. In this paper, we…
A new approach which generalizes the Selective Modal Analyis (SMA) and algorithms based upon it for solving the generalized eigenvalue problem is described. This approach allows for the systematic consideration of physical properties of the…
Unsupervised learning methods have recently shown their competitiveness against supervised training. Typically, these methods use a single objective to train the entire network. But one distinct advantage of unsupervised over supervised…
Principal Component Analysis (PCA) is a popular tool for dimensionality reduction and feature extraction in data analysis. There is a probabilistic version of PCA, known as Probabilistic PCA (PPCA). However, standard PCA and PPCA are not…
Deep reinforcement learning has demonstrated remarkable achievements across diverse domains such as video games, robotic control, autonomous driving, and drug discovery. Common methodologies in partially-observable domains largely lean on…
Neural compression is the application of neural networks and other machine learning methods to data compression. Recent advances in statistical machine learning have opened up new possibilities for data compression, allowing compression…
Sensitivity analysis (SA) is a procedure for studying how sensitive are the output results of large-scale mathematical models to some uncertainties of the input data. The models are described as a system of partial differential equations.…