We develop a primal dual active set with continuation algorithm for solving the \ell^0-regularized least-squares problem that frequently arises in compressed sensing. The algorithm couples the the primal dual active set method with a continuation strategy on the regularization parameter. At each inner iteration, it fir…
Optimal noise excitation for linear system identification reduces sample complexity.
problem Efficiently identifying linear systems with minimal data.
method Active learning algorithm using ordinary least squares and semidefinite programming.
result The proposed algorithm matches lower bounds on sample complexity for any active learning method.
FF algorithm uses goodness as a measure of input quality, derived from likelihood-ratio tests.
problem Training each layer locally with a goodness measure.
method FF algorithm uses a likelihood-ratio test to define goodness, which is the sum of squared activations normalized between layers.
result The goodness measure is a sufficient statistic for a likelihood-ratio test, explaining the FF algorithm's performance.
In the high-dimensional regression model a response variable is linearly related to p covariates, but the sample size n is smaller than p. We assume that only a small subset of covariates is `active' (i.e., the corresponding coefficients are non-zero), and consider the model-selection problem of identifying the a…
Neural networks plateau during training, identified and quantified.
problem Plateau phenomenon in gradient descent training of ReLU networks.
method Identification and quantification of plateau phenomenon; new iterative training method ANLS.
result Plateaux correspond to periods of constant activation patterns; quantification of gradient flow dynamics; characterization of stationary points.
We investigate the variety of a portfolio of stocks in normal and extreme days of market activity. We show that the variety carries information about the market activity which is not present in the single-index model and we observe that the variety time evolution is not time reversal around the crash days. We obtain th…
In this paper we address the problem of pool based active learning, and provide an algorithm, called UPAL, that works by minimizing the unbiased estimator of the risk of a hypothesis in a given hypothesis space. For the space of linear classifiers and the squared loss we show that UPAL is equivalent to an exponentially…
Analytical method finds deeper optima in two-layer ReLU networks.
problem Training two-layer ReLU networks with analytical methods.
method Analytically finding critical points of the loss function for one layer while keeping the other fixed.
result Significantly smaller training loss values on real datasets compared to gradient descent methods.
In this paper, we consider regression problems with one-hidden-layer neural networks (1NNs). We distill some properties of activation functions that lead to local strong convexity in the neighborhood of the ground-truth parameters for the 1NN squared-loss objective. Most popular nonlinear activation function…
FF algorithm uses goodness as a likelihood-ratio test for scalar normalization.
problem Training each layer locally with scalar goodness.
method FF algorithm uses a likelihood-ratio test with squared goodness as the sufficient statistic.
result The FF algorithm generalizes to anisotropic and heavy-tailed populations.
A new Universal Activation Function improves performance across various machine learning tasks.
problem Achieving near optimal performance in different machine learning tasks.
method Optimization algorithms evolve the UAF's parameters to match the optimal activation function for each task.
result The UAF converges to near optimal performance in classification, quantification, and reinforcement learning tasks.
Understanding the structure of financial markets deals with suitably determining the functional relation between financial variables. In this respect, important variables are the trading activity, defined here as the number of trades N, the traded volume V, the asset price P, the squared volatility σ2, the bid…
New activation function BrownianReLU improves LSTM network performance on financial time series.
problem Gradient instability in noisy financial time series data.
method Introduces BrownianReLU, a stochastic activation function based on Brownian motion.
result Significantly improved predictive accuracy and generalization on financial datasets.
New algorithm finds corrupted vertices in graphs with few queries.
problem Adversarial tampering of graph edges and vertices.
method Active learning algorithm with polynomial query complexity.
result Efficiently recovers corrupted vertices with small query complexity.
Active learning algorithms propose which unlabeled objects should be queried for their labels to improve a predictive model the most. We study active learners that minimize generalization bounds and uncover relationships between these bounds that lead to an improved approach to active learning. In particular we show th…
Smooth DNNs mitigate the curse of dimensionality in uniform convergence for various regression tasks.
problem The curse of dimensionality in uniform convergence of ReLU networks.
method Analysis of smoothly activated deep neural networks (smooth DNNs), establishing pseudo-dimension bounds and non-asymptotic approximation guarantees.
result Smooth DNNs achieve non-asymptotic uniform convergence rates across multiple statistical contexts, mitigating the curse of dimensionality.
We stabilize the activations of Recurrent Neural Networks (RNNs) by penalizing the squared distance between successive hidden states' norms. This penalty term is an effective regularizer for RNNs including LSTMs and IRNNs, improving performance on character-level language modeling and phoneme recognition, and outperfor…
We design an active learning algorithm for cost-sensitive multiclass classification: problems where different errors have different costs. Our algorithm, COAL, makes predictions by regressing to each label's cost and predicting the smallest. On a new example, it uses a set of regressors that perform well on past data t…
Deep learning models accurately recognize and estimate physical activity types and energy expenditure from wrist accelerometer data.
problem Rigorous evaluation of wrist-worn accelerometers for assessing physical activity across the lifespan.
method Built deep learning networks to extract spatial and temporal representations from time-series data, recognizing physical activity types and estimating energy expenditure.
result Deep learning models achieved high performance: F1 scores of 0.82, 0.81, and 95 for sedentary, locomotor, and lifestyle activities, respectively; root mean square error of 1.1 for EE estimation.
Gradient descent on ReLU networks with square loss implicitly favors balanced weights.
problem Understanding implicit regularization in nonlinear neural networks with regression losses.
method Analyzing gradient descent dynamics on ReLU networks with square loss.
result It is impossible to characterize the implicit regularization of ReLU networks with square loss by any explicit function of model parameters.
Deep ReLU networks with extra parameters have mostly good loss landscapes.
problem Finding good local minima in the loss landscape of deep neural networks.
method Analyzing shallow and deep ReLU networks with extra parameters on a generic dataset.
result Most activation patterns correspond to regions with no bad local minima.
The paper analyzes a simple neural network model with algebraic methods.
problem Finding minima of a ridge-regularized mean squared error for ReLU perceptrons.
method Developed a Divide-Enumerate-Merge strategy using computational algebra.
result Identifies both isolated and connected minima of the RR-MSE.
Optimal AFs minimize RFR test error and sensitivity.
problem Finding optimal AFs for RFR to minimize test error and sensitivity.
method Closed-form solution for AFs minimizing test error and sensitivity under different functional parsimony.
result Optimal AFs can be linear, saturated linear, or Hermite polynomial expressions.
This paper improves active learning for Gaussian process regression to handle distributional uncertainty.
problem Active learning for Gaussian process regression does not guarantee accurate predictions for target distributions.
method Proposes two methods to reduce worst-case expected error for Gaussian process regression.
result Shows an upper bound of the worst-case expected squared error, suggesting finite data labels can achieve arbitrarily small error.
In this paper, we consider parameter recovery for non-overlapping convolutional neural networks (CNNs) with multiple kernels. We show that when the inputs follow Gaussian distribution and the sample size is sufficiently large, the squared loss of such CNNs is locally strongly convex in a basin of attraction…
We analyze a simple prefiltered variation of the least squares estimator for the problem of estimation with biased, semi-parametric noise, an error model studied more broadly in causal statistics and active learning. We prove an oracle inequality which demonstrates that this procedure provably mitigates the variance in…
Efficient algorithm reduces communication costs in sparse regression.
problem Sparse linear regression with massive data.
method CESDAR algorithm, communication-efficient surrogate likelihood.
result Achieves same statistical accuracy as global estimator with reduced communication.
Active learning aims to obtain a classifier of high accuracy by using fewer label requests in comparison to passive learning by selecting effective queries. Many active learning methods have been developed in the past two decades, which sample queries based on informativeness or representativeness of unlabeled data poi…
We show that the gradient descent algorithm provides an implicit regularization effect in the learning of over-parameterized matrix factorization models and one-hidden-layer neural networks with quadratic activations. Concretely, we show that given O~(dr2) random linear measurements of a rank r positive s…
We consider the problem of online active learning to collect data for regression modeling. Specifically, we consider a decision maker with a limited experimentation budget who must efficiently learn an underlying linear population model. Our main contribution is a novel threshold-based algorithm for selection of most i…
In this paper, we consider the problem of recovering a sparse signal based on penalized least squares formulations. We develop a novel algorithm of primal-dual active set type for a class of nonconvex sparsity-promoting penalties, including ℓ0, bridge, smoothly clipped absolute deviation, capped ℓ1 and mini…
Heart rate estimation from electrocardiogram signals is very important for the early detection of cardiovascular diseases. However, due to large individual differences and varying electrocardiogram signal quality, there does not exist a single reliable estimation algorithm that works well on all subjects. Every algorit…
Efficient ANN search for sparse embeddings in ads targeting.
problem Efficiently searching near neighbors in sparse data for applications like ads targeting.
method Graph-based ANN algorithms (HNSW, chi-square two-tower model, Sign Cauchy Projections).
result Sparse embeddings and ANN algorithms improve efficiency in EBR applications.
Theory of MoE Transformers' generalization and scaling.
problem Understanding the generalization and scaling of Mixture-of-Experts (MoE) Transformers.
method Developed a theory that separates active capacity from routing combinatorics, derived a sup-norm covering-number bound, and proved a constructive approximation theorem.
result Generalization and scaling laws for MoE Transformers, showing how active capacity and routing structure affect performance.
Unified framework recovers exact input from SOM activation patterns.
problem Generating high-dimensional data from Self-Organizing Maps (SOMs).
method Inverting SOM activation patterns to recover input, using linear system and Tikhonov regularization.
result MUSIC framework produces coherent semantic transitions and maintains high classifier confidence.
The paper analyzes dynamics of momentum in high dimensions with sparse updates.
problem Theoretical analysis of momentum dynamics in high-dimensional sparse settings.
method Theoretical analysis of two models: least squares with sparse inputs and logistic regression with a rare class.
result Characterization of high-dimensional limits of momentum dynamics and phase structure.
Study shows MSE with sigmoid can match SCE in classification tasks, especially with noisy data.
problem Inconsistent errors in neural network classification tasks.
method Introduced Output Reset algorithm to use MSE with sigmoid activation.
result MSE with sigmoid activation achieves comparable accuracy and convergence rates to Softmax Cross-Entropy, especially in noisy data scenarios.
We solve ReLU regression with efficient approximations for various distributions.
problem Finding the best fitting ReLU function with square loss from unknown distributions.
method Introduced efficient constant-factor approximation algorithm and polynomial-time approximation scheme.
result First constant-factor approximation algorithm for ReLU regression with weak concentration conditions.
Improved CNN accuracy for encrypted data using approximate activation functions.
problem Low accuracy in classifying encrypted data using homomorphic encryption.
method Used a fourth-order polynomial approximation of the Swish activation function with batch normalization for homomorphic encryption.
result Achieved 99.22% accuracy on MNIST and 80.48% on CIFAR-10, improving by 0.04% and 4.11% respectively.
We consider a univariate semimartingale model for (the logarithm of) an asset price, containing jumps having possibly infinite activity (IA). The nonparametric threshold estimator of the integrated variance IV proposed in Mancini 2009 is constructed using observations on a discrete time grid, and precisely it sums up t…
Investigates least squares estimation in deterministic MoE models.
problem Complexity and difficulty in analyzing MoE models.
method Least squares estimation under deterministic MoE models.
result Rates of estimating strongly identifiable experts are faster than polynomial experts.
We propose and analyze a new family of algorithms for training neural networks with ReLU activations. Our algorithms are based on the technique of alternating minimization: estimating the activation patterns of each ReLU for all given samples, interleaved with weight updates via a least-squares step. The main focus of …
Polynomial networks converge to Gaussian processes at a rate of O(n^(-1/2)).
problem Understanding the convergence rate of polynomial networks to Gaussian processes.
method Examined one-hidden-layer neural networks with random weights, focusing on polynomial activations and their convergence rate in the 2-Wasserstein metric.
result The rate of convergence for polynomial networks to Gaussian processes is $O(n^{- rac{1}{2}})$.
The autoencoder is an effective unsupervised learning model which is widely used in deep learning. It is well known that an autoencoder with a single fully-connected hidden layer, a linear activation function and a squared error cost function trains weights that span the same subspace as the one spanned by the principa…
Latent FxLMS accelerates ANC by adapting along low-dimensional filter weights.
problem Improving active noise control with neural adaptive filters.
method Training an auto-encoder on filter coefficients, constraining weights to latent variables, and updating in latent space.
result Latent FxLMS converges in fewer steps with comparable error to standard FxLMS.
AE-LSVI identifies near-optimal policies in complex systems with minimal data.
problem Identifying near-optimal policies in complex, costly data acquisition systems.
method Combines optimism and pessimism for active exploration in a generative model setting.
result Proves near-optimal policy identification over entire state spaces with polynomial sample complexity.
Full-batch GD outperforms one-pass SGD in learning a single-index model with quadratic activation.
problem Learning a single-index model with quadratic activation using gradient descent.
method Full-batch gradient descent compared to one-pass stochastic gradient descent (SGD) on a correlation loss.
result Full-batch GD requires only n≃d samples for strong recovery, while one-pass SGD requires n≳dlogd samples. Spectral gradient methods outperform Euclidean in certain deep learning scenarios.
problem When do spectral gradient updates outperform Euclidean in deep learning?
method Layerwise condition comparing squared nuclear-to-Frobenius ratio to stable rank of activations.
result Spectral updates can be more effective than Euclidean in deep networks and transformers.