A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Study mini-batch SGD noise and its limits, proving complexity guarantees.
Improved stock return prediction model handles noise and non-stationarity.
Adam optimizer's bias is influenced by mini-batch size and momentum hyperparameters.
Adaptive Langevin dynamics reduces bias in Bayesian inference with mini-batching.
In this paper, we present a new practical method for Bayesian learning that can rapidly draw representative samples from complex posterior distributions with multiple isolated modes in the presence of mini-batch noise. This is achieved by simulating a collection of replicas in parallel with different temperatures and p…
Improved SHB method for faster convergence on strongly-convex quadratics.
Deep neural networks (DNNs) for supervised learning can be viewed as a pipeline of a feature extractor (i.e. last hidden layer) and a linear classifier (i.e. output layer) that is trained jointly with stochastic gradient descent (SGD). In each iteration of SGD, a mini-batch from the training data is sampled and the tru…
Stochastic Gradient Descent introduces noise in training, affecting model decision boundaries.
New bounds for KANs trained with DP-SGD, addressing correlated noise.
Study shows gradient variance increases during deep learning training, contrary to common belief.
Mini-batch sub-sampling in neural network training is unavoidable, due to growing data demands, memory-limited computational resources such as graphical processing units (GPUs), and the dynamics of on-line learning. In this study we specifically distinguish between static mini-batch sub-sampled loss functions, where mi…
Nonlinear SGD achieves high-probability rates in non-convex optimization with heavy-tailed noise.
Fast robust subspace tracking in sparse data-dependent noise with near-optimal delay.
Noise in SGD affects overparameterized models, favoring sparse solutions.
New algorithms improve optimization under varying noise.
Mini-batch SGD with momentum is a fundamental algorithm for learning large predictive models. In this paper we develop a new analytic framework to analyze noise-averaged properties of mini-batch SGD for linear models at constant learning rates, momenta and sizes of batches. Our key idea is to consider the dynamics of t…
Numerous empirical evidence has corroborated that the noise plays a crucial rule in effective and efficient training of neural networks. The theory behind, however, is still largely unknown. This paper studies this fundamental problem through training a simple two-layer convolutional neural network model. Although trai…
Improved stochastic gradient estimation for deep learning in high dimensions.
We propose a new sampler that integrates the protocol of parallel tempering with the Nosé-Hoover (NH) dynamics. The proposed method can efficiently draw representative samples from complex posterior distributions with multiple isolated modes in the presence of noise arising from stochastic gradient. It potentially faci…
The gradient noise of SGD is considered to play a central role in the observed strong generalization abilities of deep learning. While past studies confirm that the magnitude and the covariance structure of gradient noise are critical for regularization, it remains unclear whether or not the class of noise distribution…
We model how Lipschitz continuity changes during neural network training.
A new method for deep learning imbalance or noise, ABSGD, improves efficiency and effectiveness.
New method reduces variance in stochastic optimization with high confidence.
DAIS improves AIS for differentiable marginal likelihood estimation.
A new algorithm is proposed which accelerates the mini-batch k-means algorithm of Sculley (2010) by using the distance bounding approach of Elkan (2003). We argue that, when incorporating distance bounds into a mini-batch algorithm, already used data should preferentially be reused. To this end we propose using nested …
Method reweights instances and classes to improve robustness in noisy data.
This work characterizes the benefits of averaging schemes widely used in conjunction with stochastic gradient descent (SGD). In particular, this work provides a sharp analysis of: (1) mini-batching, a method of averaging many samples of a stochastic gradient to both reduce the variance of the stochastic gradient estima…
Proposes m-POT to improve m-OT's misspecified mappings issue.
To deal with very large datasets a mini-batch version of the Monte Carlo Markov Chain Stochastic Approximation Expectation-Maximization algorithm for general latent variable models is proposed. For exponential models the algorithm is shown to be convergent under classicalconditions as the number of iterations increases…
New streaming methods improve convergence rates for optimization problems.
Modern deep neural network training is typically based on mini-batch stochastic gradient optimization. While the use of large mini-batches increases the available computational parallelism, small batch training has been shown to provide improved generalization performance and allows a significantly smaller memory footp…
AlignFlow improves FGMs by optimizing noise and data alignment.
A new method for mini-batch optimal transport improves scalability and accuracy.
With the large rising of complex data, the nonconvex models such as nonconvex loss function and nonconvex regularizer are widely used in machine learning and pattern recognition. In this paper, we propose a class of mini-batch stochastic ADMMs (alternating direction method of multipliers) for solving large-scale noncon…
We study a mini-batch diversification scheme for stochastic gradient descent (SGD). While classical SGD relies on uniformly sampling data points to form a mini-batch, we propose a non-uniform sampling scheme based on the Determinantal Point Process (DPP). The DPP relies on a similarity measure between data points and g…
In this paper, we develop a new accelerated stochastic gradient method for efficiently solving the convex regularized empirical risk minimization problem in mini-batch settings. The use of mini-batches is becoming a golden standard in the machine learning community, because mini-batch settings stabilize the gradient es…
Federated multi-mini-batch improves efficiency in non-IID environments.
Paper analyzes gradient descent with noisy data copies for linear regression, showing regularization and acceleration effects.
Study shows how mini-batch GD with random reshuffling affects least squares regression dynamics.
We present a generic framework for trading off fidelity and cost in computing stochastic gradients when the costs of acquiring stochastic gradients of different quality are not known a priori. We consider a mini-batch oracle that distributes a limited query budget over a number of stochastic gradients and aggregates th…
We provide tight finite-time convergence bounds for gradient descent and stochastic gradient descent on quadratic functions, when the gradients are delayed and reflect iterates from rounds ago. First, we show that without stochastic noise, delays strongly affect the attainable optimization error: In fact, the error…
CWGD measures gradient diversity weighted by curvature, improving SGD convergence.
Class2Simi reduces noise in noisy label learning by transforming noisy class labels into noisy similarity labels.
We propose a general yet simple theorem describing the convergence of SGD under the arbitrary sampling paradigm. Our theorem describes the convergence of an infinite array of variants of SGD, each of which is associated with a specific probability law governing the data selection rule used to form mini-batches. This is…
Improved robustness in optimization methods using second-order information.
In this work we develop a new algorithm for regularized empirical risk minimization. Our method extends recent techniques of Shalev-Shwartz [02/2015], which enable a dual-free analysis of SDCA, to arbitrary mini-batching schemes. Moreover, our method is able to better utilize the information in the data defining the ER…
In this paper we aim to formally explain the phenomenon of fast convergence of SGD observed in modern machine learning. The key observation is that most modern learning architectures are over-parametrized and are trained to interpolate the data by driving the empirical loss (classification and regression) close to zero…
In statistical learning for real-world large-scale data problems, one must often resort to "streaming" algorithms which operate sequentially on small batches of data. In this work, we present an analysis of the information-theoretic limits of mini-batch inference in the context of generalized linear models and low-rank…