arXiv research

This paper analyzes a simplified strategy for nonlinear control using local linear models and iLQR updates.

We introduce Embed to Control (E2C), a method for model learning and control of non-linear dynamical systems from raw pixel images. E2C consists of a deep generative model, belonging to the family of variational autoencoders, that learns to generate image trajectories from a latent space in which the dynamics is constr…

We show LLMs can be locally linear, enabling better control of activations.

A new approach predicts next observations without explicit decoding for better control.

Breaks down complex nonlinear dynamics into simpler components.

Many real-world sequential decision-making problems can be formulated as optimal control with high-dimensional observations and unknown dynamics. A promising approach is to embed the high-dimensional observations into a lower-dimensional latent representation space, estimate the latent dynamics model, then utilize this…

We investigate finite-time decoupled convergence in nonlinear two-time-scale stochastic approximation.

Background: Functional magnetic resonance imaging (fMRI) provides non-invasive measures of neuronal activity using an endogenous Blood Oxygenation-Level Dependent (BOLD) contrast. This article introduces a nonlinear dimensionality reduction (Locally Linear Embedding) to extract informative measures of the underlying ne…

New classifier combines locally linear kernels for fast and accurate non-linear classification.

We introduce the Locally Linear Latent Variable Model (LL-LVM), a probabilistic model for non-linear manifold discovery that describes a joint distribution over observations, their manifold coordinates and locally linear maps conditioned on a set of neighbourhood relationships. The model allows straightforward variatio…

This paper discusses topological and locally linear actions of finite groups on $S^4$. Local linearity of the orientation preserving actions on $S^4$ forces the group to be a subgroup of $SO(5)$. On the other hand, orientation reversing topological actions of "exotic" groups $G$ (i.e. $G\not\subset O(5)$) on $S^4$ are …

New algorithm reduces control error in systems with changing dynamics.

This paper simplifies deep ReLU networks into local linear models for better interpretability.

The network Lasso (nLasso) has been proposed recently as an efficient learning algorithm for massive networked data sets (big data over networks). It extends the well-known least absolute shrinkage and selection operator (Lasso) from learning sparse (generalized) linear models to network models. Efficient implementatio…

Study proposes Local Linear Encoding for better feature discretization.

A new method simplifies HLLE for better robustness.

LLE produces unwanted results without regularization, which can be prevented with regularization.

Most of existing manifold learning methods rely on Mean Squared Error (MSE) or $\ell_2$ norm. However, for the problem of image quality assessment, these are not promising measure. In this paper, we introduce the concept of an image structure manifold which captures image structure features and discriminates image dist…

In this paper, we propose and study random maxout features, which are constructed by first projecting the input data onto sets of randomly generated vectors with Gaussian elements, and then outputing the maximum projection value for each set. We show that the resulting random feature map, when used in conjunction with …

The paper develops predictors for functional data on manifolds.

New insights into continual learning for deep models, showing convergence issues but local linear solutions.

Existing works on "black-box" model interpretation use local-linear approximations to explain the predictions made for each data instance in terms of the importance assigned to the different features for arriving at the prediction. These works provide instancewise explanations and thus give a local view of the model. T…

Survey of Locally Linear Embedding and its variants.

Cyclic coordinate descent identifies models in finite time and converges linearly.

New method disentangles perceptual uncertainty and behavioral costs in partially observable systems.

This paper improves Bayesian neural nets by using local linearization.

S.Bauer and M.Furuta defined a stable cohomotopy refinement of the Seiberg-Witten invariants. In this paper, we prove a vanishing theorem of Bauer-Furuta invariants for 4-manifolds with smooth Z/2-actions. As an application, we give a constraint on smooth Z/2-actions on homotopy K3#K3, and construct a nonsmoothable loc…

Foundational brain dynamics model using stochastic optimal control.

Policy gradient converges linearly with Hadamard parameterization in tabular settings.

Local Linear embedding (LLE) is a popular dimension reduction method. In this paper, we first show LLE with nonnegative constraint is equivalent to the widely used Laplacian embedding. We further propose to iterate the two steps in LLE repeatedly to improve the results. Thirdly, we relax the kNN constraint of LLE and p…

This paper develops a new method to model treatment effects that are heterogeneous across different quantiles.

Following the programme set out in Part I of this work, we develop a conceptual higher order differential calculus. The '' local linear algebra '' defined in Part I is generalized by '' higher order local linear algebra ''. The underlying combinatorial object of such higher algebra is the natural n-dimensional hyper-cu…

Paper proposes CARL for better control in RL from sensory data.

MixUp is a recently proposed data-augmentation scheme, which linearly interpolates a random pair of training examples and correspondingly the one-hot representations of their labels. Training deep neural networks with such additional data is shown capable of significantly improving the predictive accuracy of the curren…

Random forests are a powerful method for non-parametric regression, but are limited in their ability to fit smooth signals, and can show poor predictive performance in the presence of strong, smooth effects. Taking the perspective of random forests as an adaptive kernel method, we pair the forest kernel with a local li…

In this paper we implement a Local Linear Regression Ensemble Committee (LOLREC) to predict 1-day-ahead returns of 453 assets form the S&P500. The estimates and the historical returns of the committees are used to compute the weights of the portfolio from the 453 stock. The proposed method outperforms benchmark portfol…

New GP model estimates piecewise continuous functions.

Generative LLE modifies LLE to generate stochastic embeddings.

Study shows DNNs can recover functions with fewer samples than model parameters at overparameterization.

New measure EC assesses node contributions in nonlinear, time-varying systems.

NGSLL combines DNN accuracy with linear model interpretability.

This work connects LLE, factor analysis, and probabilistic PCA through a stochastic perspective.

Folded concave penalization methods have been shown to enjoy the strong oracle property for high-dimensional sparse estimation. However, a folded concave penalization problem usually has multiple local solutions and the oracle property is established only for one of the unknown local solutions. A challenging fundamenta…

BART and MOTR-BART improve tree-based predictions with local linear models.

Proposes a boundary detection method inspired by LLE for high-dimensional data.

Gradient method converges locally linearly for overparameterized Gaussian mixtures.

The Gronwall conjecture states that a planar 3-web of foliations which admits more than one distinct linearizations is locally equivalent to an algebraic web. We propose an analogue of the Gronwall conjecture for the 3-web of foliations by Legendrian curves in a contact three manifold. The Legendrian Gronwall conjectur…

Flexible Kernels for Protein Property Prediction