arXiv research

This work identifies redundant tests in conditional-independence-based discovery that can improve graphical model accuracy.

We show that the error probability of reconstructing kernel matrices from Random Fourier Features for the Gaussian kernel function is at most $\mathcal{O}(R^{2/3} \exp(-D))$, where $D$ is the number of random features and $R$ is the diameter of the data domain. We also provide an information-theoretic method-independen…

New method detects causal relationships from noisy measurements.

Sequential Kernel-based Conditional Independence Testing via Adaptive Betting

In this paper we consider portmanteau tests for testing the adequacy of multiplicative seasonal autoregressive moving-average (SARMA) models under the assumption that the errors are uncorrelated but not necessarily independent.We relax the standard independence assumption on the error term in order to extend the range …

Redundancy in AI perception systems doesn't guarantee independent error occurrences.

Paper extends nonparametric regression bounds for dependent $\beta$-mixing samples.

Deep ReLU networks generalize well with few parameters.

New insights into CI tests reveal key factors for practical performance.

New bounds on majority voting's accuracy for multi-class classification problems.

New EiV models correct bias in operator learning with noisy data.

New bounds for SGLD show error decreases with more data.

Boosting algorithm reduces error in noisy data.

In this paper, we prove that some Gaussian structural equation models with dependent errors having equal variances are identifiable from their corresponding Gaussian distributions. Specifically, we prove identifiability for the Gaussian structural equation models that can be represented as Andersson-Madigan-Perlman cha…

Study of supervised learning from multiple non-independent sequences.

We find a deterministic equivalent for random feature regression's test error, independent of feature map dimension.

Paper develops streaming algorithms to estimate classifier accuracy on unlabeled data.

We show how to estimate a model's test error from unlabeled data, on distributions very different from the training distribution, while assuming only that certain conditional independencies are preserved between train and test. We do not need to assume that the optimal predictor is the same between train and test, or t…

Suppose that we observe $y \in \mathbb{R}^f$ and $X \in \mathbb{R}^{f \times m}$ in the following errors-in-variables model: \begin{eqnarray*} y & = & X_0 β^* + ε\\ X & = & X_0 + W \end{eqnarray*} where $X_0$ is a $f \times m$ design matrix with independent subgaussian row vectors, $ε\in \mathbb{R}^f$ is a noise vector…

The paper introduces a method to model error correlations in multivariate time series forecasting.

New methods for CI testing under model misspecification.

DIET tests conditional independence using marginal dependence measures of residual information.

New bounds for neural networks without loss boundedness assumption.

Bayesian method recovers causal structure in SEMs with equal error variances.

New method uses CDMs to improve CI testing without distributional assumptions.

In this paper, we improve the PAC-Bayesian error bound for linear regression derived in Germain et al. [10]. The improvements are twofold. First, the proposed error bound is tighter, and converges to the generalization loss with a well-chosen temperature parameter. Second, the error bound also holds for training data t…

Paper relaxes independence assumption for non-centered data.

New test for conditional independence using kernel embeddings.

Study high-dimensional logistic regression with missing data, providing exact error characterizations.

New method tests independence using ROC analysis and bipartite ranking.

Novel bounds for SGLD show generalization error decreases with more samples.

Using methods of statistical physics, we analyse the error of learning couplings in large Ising models from independent data (the inverse Ising problem). We concentrate on learning based on local cost functions, such as the pseudo-likelihood method for which the couplings are inferred independently for each spin. Assum…

Paper analyzes online tensorial ICA convergence with stochastic approximation.

Suppose that we observe $y \in \mathbb{R}^n$ and $X \in \mathbb{R}^{n \times m}$ in the following errors-in-variables model: \begin{eqnarray*} y & = & X_0 β^* +ε\\ X & = & X_0 + W, \end{eqnarray*} where $X_0$ is an $n \times m$ design matrix with independent subgaussian row vectors, $ε\in \mathbb{R}^n$ is a noise vecto…

Data-independent pruning method reduces neural network size with accuracy guarantees.

Paper introduces a new cost function to improve deep learning model generalization.

Robustly estimates mean in incomplete data with corrupted examples.

We study the problem of {\em distribution-independent} PAC learning of halfspaces in the presence of Massart noise. Specifically, we are given a set of labeled examples $(\mathbf{x}, y)$ drawn from a distribution $\mathcal{D}$ on $\mathbb{R}^{d+1}$ such that the marginal distribution on the unlabeled points $\mathbf{x}…

Stagewise training strategy is widely used for learning neural networks, which runs a stochastic algorithm (e.g., SGD) starting with a relatively large step size (aka learning rate) and geometrically decreasing the step size after a number of iterations. It has been observed that the stagewise SGD has much faster conve…

Optimizes embedding accuracy for data variance and error.

SGD reduces test error by decorrelating updates.

Estimates error for robust M-estimators with convex penalties.

SGD handles label noise with bounds improving over SGLD.

Study of estimation errors in surrogate loss minimizers, providing stronger guarantees than existing methods.

Study error bounds and optimal schedules for Masked Diffusions with factorized approximations.

We show that if $F$ is a convex class of functions that is $L$-subgaussian, the error rate of learning problems generated by independent noise is equivalent to a fixed point determined by `local' covering estimates of the class, rather than by the gaussian averages. To that end, we establish new sharp upper and lower e…

We have developed an automatic sleep stage classification algorithm based on deep residual neural networks and raw polysomnogram signals. Briefly, the raw data is passed through 50 convolutional layers before subsequent classification into one of five sleep stages. Three model configurations were trained on 1850 polyso…

The paper develops robust tests for detecting independence in synchronous stochastic systems with finite sample guarantees.