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Found 131 papers, 25 papers with code
REBEL: Reinforcement Learning via Regressing Relative Rewards
While originally developed for continuous control problems, Proximal Policy Optimization (PPO) has emerged as the work-horse of a variety of reinforcement learning (RL) applications including the fine-tuning of generative models.
Dataset Reset Policy Optimization for RLHF
Motivated by the fact that offline preference dataset provides informative states (i. e., data that is preferred by the labelers), our new algorithm, Dataset Reset Policy Optimization (DR-PO), integrates the existing offline preference dataset into the online policy training procedure via dataset reset: it directly resets the policy optimizer to the states in the offline dataset, instead of always starting from the initial state distribution.
Horizon-Free Regret for Linear Markov Decision Processes
A recent line of works showed regret bounds in reinforcement learning (RL) can be (nearly) independent of planning horizon, a. k. a.~the horizon-free bounds.
Computational-Statistical Gaps in Gaussian Single-Index Models
Single-Index Models are high-dimensional regression problems with planted structure, whereby labels depend on an unknown one-dimensional projection of the input via a generic, non-linear, and potentially non-deterministic transformation.
How Well Can Transformers Emulate In-context Newton's Method?
Recent studies have suggested that Transformers can implement first-order optimization algorithms for in-context learning and even second order ones for the case of linear regression.
How Transformers Learn Causal Structure with Gradient Descent
The key insight of our proof is that the gradient of the attention matrix encodes the mutual information between tokens.
LoRA Training in the NTK Regime has No Spurious Local Minima
Low-rank adaptation (LoRA) has become the standard approach for parameter-efficient fine-tuning of large language models (LLM), but our theoretical understanding of LoRA has been limited.
Revisiting Zeroth-Order Optimization for Memory-Efficient LLM Fine-Tuning: A Benchmark
In the evolving landscape of natural language processing (NLP), fine-tuning pre-trained Large Language Models (LLMs) with first-order (FO) optimizers like SGD and Adam has become standard.
BitDelta: Your Fine-Tune May Only Be Worth One Bit
Large Language Models (LLMs) are typically trained in two phases: pre-training on large internet-scale datasets, and fine-tuning for downstream tasks.
An Information-Theoretic Analysis of In-Context Learning
Previous theoretical results pertaining to meta-learning on sequences build on contrived assumptions and are somewhat convoluted.
Medusa: Simple LLM Inference Acceleration Framework with Multiple Decoding Heads
We present two levels of fine-tuning procedures for Medusa to meet the needs of different use cases: Medusa-1: Medusa is directly fine-tuned on top of a frozen backbone LLM, enabling lossless inference acceleration.
Towards Optimal Statistical Watermarking
Key to our formulation is a coupling of the output tokens and the rejection region, realized by pseudo-random generators in practice, that allows non-trivial trade-offs between the Type I error and Type II error.
Optimal Multi-Distribution Learning
Focusing on a hypothesis class of Vapnik-Chervonenkis (VC) dimension $d$, we propose a novel algorithm that yields an $varepsilon$-optimal randomized hypothesis with a sample complexity on the order of $(d+k)/\varepsilon^2$ (modulo some logarithmic factor), matching the best-known lower bound.
Dichotomy of Early and Late Phase Implicit Biases Can Provably Induce Grokking
Recent work by Power et al. (2022) highlighted a surprising "grokking" phenomenon in learning arithmetic tasks: a neural net first "memorizes" the training set, resulting in perfect training accuracy but near-random test accuracy, and after training for sufficiently longer, it suddenly transitions to perfect test accuracy.
Learning Hierarchical Polynomials with Three-Layer Neural Networks
Our main result shows that for a large subclass of degree $k$ polynomials $p$, a three-layer neural network trained via layerwise gradient descent on the square loss learns the target $h$ up to vanishing test error in $\widetilde{\mathcal{O}}(d^k)$ samples and polynomial time.
Provably Efficient CVaR RL in Low-rank MDPs
We study CVaR RL in low-rank MDPs with nonlinear function approximation.
REST: Retrieval-Based Speculative Decoding
We introduce Retrieval-Based Speculative Decoding (REST), a novel algorithm designed to speed up language model generation.
Settling the Sample Complexity of Online Reinforcement Learning
While a number of recent works achieved asymptotically minimal regret in online RL, the optimality of these results is only guaranteed in a ``large-sample'' regime, imposing enormous burn-in cost in order for their algorithms to operate optimally.
Teaching Arithmetic to Small Transformers
Even in the complete absence of pretraining, this approach significantly and simultaneously improves accuracy, sample complexity, and convergence speed.
Scaling In-Context Demonstrations with Structured Attention
However, their capabilities of in-context learning are limited by the model architecture: 1) the use of demonstrations is constrained by a maximum sentence length due to positional embeddings; 2) the quadratic complexity of attention hinders users from using more demonstrations efficiently; 3) LLMs are shown to be sensitive to the order of the demonstrations.
Sample Complexity for Quadratic Bandits: Hessian Dependent Bounds and Optimal Algorithms
We consider a fundamental setting in which the objective function is quadratic, and provide the first tight characterization of the optimal Hessian-dependent sample complexity.
Solving Robust MDPs through No-Regret Dynamics
Reinforcement Learning is a powerful framework for training agents to navigate different situations, but it is susceptible to changes in environmental dynamics.
Provable Reward-Agnostic Preference-Based Reinforcement Learning
Preference-based Reinforcement Learning (PbRL) is a paradigm in which an RL agent learns to optimize a task using pair-wise preference-based feedback over trajectories, rather than explicit reward signals.
Reward Collapse in Aligning Large Language Models
This insight allows us to derive closed-form expressions for the reward distribution associated with a set of utility functions in an asymptotic regime.
Fine-Tuning Language Models with Just Forward Passes
Fine-tuning language models (LMs) has yielded success on diverse downstream tasks, but as LMs grow in size, backpropagation requires a prohibitively large amount of memory.
Provable Offline Preference-Based Reinforcement Learning
Our proposed algorithm consists of two main steps: (1) estimate the implicit reward using Maximum Likelihood Estimation (MLE) with general function approximation from offline data and (2) solve a distributionally robust planning problem over a confidence set around the MLE.
Local Optimization Achieves Global Optimality in Multi-Agent Reinforcement Learning
Motivated by the observation, we present a multi-agent PPO algorithm in which the local policy of each agent is updated similarly to vanilla PPO.
Can We Find Nash Equilibria at a Linear Rate in Markov Games?
Second, when both players adopt the algorithm, their joint policy converges to a Nash equilibrium of the game.
Provably Efficient Reinforcement Learning via Surprise Bound
Value function approximation is important in modern reinforcement learning (RL) problems especially when the state space is (infinitely) large.
Efficient displacement convex optimization with particle gradient descent
Particle gradient descent, which uses particles to represent a probability measure and performs gradient descent on particles in parallel, is widely used to optimize functions of probability measures.
Looped Transformers as Programmable Computers
We present a framework for using transformer networks as universal computers by programming them with specific weights and placing them in a loop.
Understanding Incremental Learning of Gradient Descent: A Fine-grained Analysis of Matrix Sensing
It is believed that Gradient Descent (GD) induces an implicit bias towards good generalization in training machine learning models.
Reconstructing Training Data from Model Gradient, Provably
Understanding when and how much a model gradient leaks information about the training sample is an important question in privacy.
From Gradient Flow on Population Loss to Learning with Stochastic Gradient Descent
When these potentials further satisfy certain self-bounding properties, we show that they can be used to provide a convergence guarantee for Gradient Descent (GD) and SGD (even when the paths of GF and GD/SGD are quite far apart).
Self-Stabilization: The Implicit Bias of Gradient Descent at the Edge of Stability
Our analysis provides precise predictions for the loss, sharpness, and deviation from the PGD trajectory throughout training, which we verify both empirically in a number of standard settings and theoretically under mild conditions.
PAC Reinforcement Learning for Predictive State Representations
We show that given a realizable model class, the sample complexity of learning the near optimal policy only scales polynomially with respect to the statistical complexity of the model class, without any explicit polynomial dependence on the size of the state and observation spaces.
Neural Networks can Learn Representations with Gradient Descent
Furthermore, in a transfer learning setup where the data distributions in the source and target domain share the same representation $U$ but have different polynomial heads we show that a popular heuristic for transfer learning has a target sample complexity independent of $d$.
Provably Efficient Reinforcement Learning in Partially Observable Dynamical Systems
We study Reinforcement Learning for partially observable dynamical systems using function approximation.
Computationally Efficient PAC RL in POMDPs with Latent Determinism and Conditional Embeddings
We show our algorithm's computational and statistical complexities scale polynomially with respect to the horizon and the intrinsic dimension of the feature on the observation space.
Identifying good directions to escape the NTK regime and efficiently learn low-degree plus sparse polynomials
Next, we show that a wide two-layer neural network can jointly use the NTK and QuadNTK to fit target functions consisting of a dense low-degree term and a sparse high-degree term -- something neither the NTK nor the QuadNTK can do on their own.
Decentralized Optimistic Hyperpolicy Mirror Descent: Provably No-Regret Learning in Markov Games
We study decentralized policy learning in Markov games where we control a single agent to play with nonstationary and possibly adversarial opponents.
On the Effective Number of Linear Regions in Shallow Univariate ReLU Networks: Convergence Guarantees and Implicit Bias
We study the dynamics and implicit bias of gradient flow (GF) on univariate ReLU neural networks with a single hidden layer in a binary classification setting.
Nearly Minimax Algorithms for Linear Bandits with Shared Representation
We give novel algorithms for multi-task and lifelong linear bandits with shared representation.
Offline Reinforcement Learning with Realizability and Single-policy Concentrability
Sample-efficiency guarantees for offline reinforcement learning (RL) often rely on strong assumptions on both the function classes (e. g., Bellman-completeness) and the data coverage (e. g., all-policy concentrability).
Optimization-Based Separations for Neural Networks
Depth separation results propose a possible theoretical explanation for the benefits of deep neural networks over shallower architectures, establishing that the former possess superior approximation capabilities.
Provable Hierarchy-Based Meta-Reinforcement Learning
To address this gap, we analyze HRL in the meta-RL setting, where a learner learns latent hierarchical structure during meta-training for use in a downstream task.
Provable Regret Bounds for Deep Online Learning and Control
The theory of deep learning focuses almost exclusively on supervised learning, non-convex optimization using stochastic gradient descent, and overparametrized neural networks.
MURO: Deployment Constrained Reinforcement Learning with Model-based Uncertainty Regularized Batch Optimization
In the high support region (low uncertainty), we encourage our policy by taking an aggressive update.
Towards General Function Approximation in Zero-Sum Markov Games
In the {coordinated} setting where both players are controlled by the agent, we propose a model-based algorithm and a model-free algorithm.
Going Beyond Linear RL: Sample Efficient Neural Function Approximation
While the theory of RL has traditionally focused on linear function approximation (or eluder dimension) approaches, little is known about nonlinear RL with neural net approximations of the Q functions.
Optimal Gradient-based Algorithms for Non-concave Bandit Optimization
This work considers a large family of bandit problems where the unknown underlying reward function is non-concave, including the low-rank generalized linear bandit problems and two-layer neural network with polynomial activation bandit problem.
A Short Note on the Relationship of Information Gain and Eluder Dimension
Eluder dimension and information gain are two widely used methods of complexity measures in bandit and reinforcement learning.
Near-Optimal Linear Regression under Distribution Shift
Transfer learning is essential when sufficient data comes from the source domain, with scarce labeled data from the target domain.
Label Noise SGD Provably Prefers Flat Global Minimizers
In overparametrized models, the noise in stochastic gradient descent (SGD) implicitly regularizes the optimization trajectory and determines which local minimum SGD converges to.
Policy Mirror Descent for Regularized Reinforcement Learning: A Generalized Framework with Linear Convergence
These can often be accounted for via regularized RL, which augments the target value function with a structure-promoting regularizer.
How Fine-Tuning Allows for Effective Meta-Learning
Representation learning has been widely studied in the context of meta-learning, enabling rapid learning of new tasks through shared representations.
Bilinear Classes: A Structural Framework for Provable Generalization in RL
The framework incorporates nearly all existing models in which a polynomial sample complexity is achievable, and, notably, also includes new models, such as the Linear $Q^*/V^*$ model in which both the optimal $Q$-function and the optimal $V$-function are linear in some known feature space.
MUSBO: Model-based Uncertainty Regularized and Sample Efficient Batch Optimization for Deployment Constrained Reinforcement Learning
We consider a setting that lies between pure offline reinforcement learning (RL) and pure online RL called deployment constrained RL in which the number of policy deployments for data sampling is limited.
A Theory of Label Propagation for Subpopulation Shift
In this work, we propose a provably effective framework for domain adaptation based on label propagation.
Provably Efficient Policy Optimization for Two-Player Zero-Sum Markov Games
Policy-based methods with function approximation are widely used for solving two-player zero-sum games with large state and/or action spaces.
How to Characterize The Landscape of Overparameterized Convolutional Neural Networks
With the help of a new technique called {\it neural network grafting}, we demonstrate that even during the entire training process, feature distributions of differently initialized networks remain similar at each layer.
Agnostic $Q$-learning with Function Approximation in Deterministic Systems: Near-Optimal Bounds on Approximation Error and Sample Complexity
The current paper studies the problem of agnostic $Q$-learning with function approximation in deterministic systems where the optimal $Q$-function is approximable by a function in the class $\mathcal{F}$ with approximation error $\delta \ge 0$.
Beyond Lazy Training for Over-parameterized Tensor Decomposition
We show that in a lazy training regime (similar to the NTK regime for neural networks) one needs at least $m = \Omega(d^{l-1})$, while a variant of gradient descent can find an approximate tensor when $m = O^*(r^{2. 5l}\log d)$.
Impact of Representation Learning in Linear Bandits
For the finite-action setting, we present a new algorithm which achieves $\widetilde{O}(T\sqrt{kN} + \sqrt{dkNT})$ regret, where $N$ is the number of rounds we play for each bandit.
How Important is the Train-Validation Split in Meta-Learning?
A common practice in meta-learning is to perform a train-validation split (\emph{train-val method}) where the prior adapts to the task on one split of the data, and the resulting predictor is evaluated on another split.
Sanity-Checking Pruning Methods: Random Tickets can Win the Jackpot
In this paper, we conduct sanity checks for the above beliefs on several recent unstructured pruning methods and surprisingly find that: (1) A set of methods which aims to find good subnetworks of the randomly-initialized network (which we call "initial tickets"), hardly exploits any information from the training data; (2) For the pruned networks obtained by these methods, randomly changing the preserved weights in each layer, while keeping the total number of preserved weights unchanged per layer, does not affect the final performance.
Generalized Leverage Score Sampling for Neural Networks
Leverage score sampling is a powerful technique that originates from theoretical computer science, which can be used to speed up a large number of fundamental questions, e. g. linear regression, linear programming, semi-definite programming, cutting plane method, graph sparsification, maximum matching and max-flow.
Predicting What You Already Know Helps: Provable Self-Supervised Learning
Self-supervised representation learning solves auxiliary prediction tasks (known as pretext tasks) without requiring labeled data to learn useful semantic representations.
Implicit Bias in Deep Linear Classification: Initialization Scale vs Training Accuracy
We provide a detailed asymptotic study of gradient flow trajectories and their implicit optimization bias when minimizing the exponential loss over "diagonal linear networks".
Modeling from Features: a Mean-field Framework for Over-parameterized Deep Neural Networks
This new representation overcomes the degenerate situation where all the hidden units essentially have only one meaningful hidden unit in each middle layer, and further leads to a simpler representation of DNNs, for which the training objective can be reformulated as a convex optimization problem via suitable re-parameterization.
Towards Understanding Hierarchical Learning: Benefits of Neural Representations
When the trainable network is the quadratic Taylor model of a wide two-layer network, we show that neural representation can achieve improved sample complexities compared with the raw input: For learning a low-rank degree-$p$ polynomial ($p \geq 4$) in $d$ dimension, neural representation requires only $\tilde{O}(d^{\lceil p/2 \rceil})$ samples, while the best-known sample complexity upper bound for the raw input is $\tilde{O}(d^{p-1})$.
Convergence of Meta-Learning with Task-Specific Adaptation over Partial Parameters
Although model-agnostic meta-learning (MAML) is a very successful algorithm in meta-learning practice, it can have high computational cost because it updates all model parameters over both the inner loop of task-specific adaptation and the outer-loop of meta initialization training.
Shape Matters: Understanding the Implicit Bias of the Noise Covariance
We show that in an over-parameterized setting, SGD with label noise recovers the sparse ground-truth with an arbitrary initialization, whereas SGD with Gaussian noise or gradient descent overfits to dense solutions with large norms.
Distributed Estimation for Principal Component Analysis: an Enlarged Eigenspace Analysis
To abandon this eigengap assumption, we consider a new route in our analysis: instead of exactly identifying the top-$L$-dim eigenspace, we show that our estimator is able to cover the targeted top-$L$-dim population eigenspace.
Steepest Descent Neural Architecture Optimization: Escaping Local Optimum with Signed Neural Splitting
Recently, Liu et al.[19] proposed a splitting steepest descent (S2D) method that jointly optimizes the neural parameters and architectures based on progressively growing network structures by splitting neurons into multiple copies in a steepest descent fashion.
Few-Shot Learning via Learning the Representation, Provably
First, we study the setting where this common representation is low-dimensional and provide a fast rate of $O\left(\frac{\mathcal{C}\left(\Phi\right)}{n_1T} + \frac{k}{n_2}\right)$; here, $\Phi$ is the representation function class, $\mathcal{C}\left(\Phi\right)$ is its complexity measure, and $k$ is the dimension of the representation.
Kernel and Rich Regimes in Overparametrized Models
We provide a complete and detailed analysis for a family of simple depth-$D$ models that already exhibit an interesting and meaningful transition between the kernel and rich regimes, and we also demonstrate this transition empirically for more complex matrix factorization models and multilayer non-linear networks.
Agnostic Q-learning with Function Approximation in Deterministic Systems: Tight Bounds on Approximation Error and Sample Complexity
2) In conjunction with the lower bound in [Wen and Van Roy, NIPS 2013], our upper bound suggests that the sample complexity $\widetilde{\Theta}\left(\mathrm{dim}_E\right)$ is tight even in the agnostic setting.
Neural Temporal-Difference Learning Converges to Global Optima
Temporal-difference learning (TD), coupled with neural networks, is among the most fundamental building blocks of deep reinforcement learning.
When Does Non-Orthogonal Tensor Decomposition Have No Spurious Local Minima?
We study the optimization problem for decomposing $d$ dimensional fourth-order Tensors with $k$ non-orthogonal components.
SGD Learns One-Layer Networks in WGANs
Generative adversarial networks (GANs) are a widely used framework for learning generative models.
Beyond Linearization: On Quadratic and Higher-Order Approximation of Wide Neural Networks
Recent theoretical work has established connections between over-parametrized neural networks and linearized models governed by he Neural Tangent Kernels (NTKs).
Optimal transport mapping via input convex neural networks
Building upon recent advances in the field of input convex neural networks, we propose a new framework where the gradient of one convex function represents the optimal transport mapping.
On the Theory of Policy Gradient Methods: Optimality, Approximation, and Distribution Shift
Policy gradient methods are among the most effective methods in challenging reinforcement learning problems with large state and/or action spaces.
Convergence of Adversarial Training in Overparametrized Neural Networks
Neural networks are vulnerable to adversarial examples, i. e. inputs that are imperceptibly perturbed from natural data and yet incorrectly classified by the network.
Neural Temporal-Difference and Q-Learning Provably Converge to Global Optima
Temporal-difference learning (TD), coupled with neural networks, is among the most fundamental building blocks of deep reinforcement learning.
Lexicographic and Depth-Sensitive Margins in Homogeneous and Non-Homogeneous Deep Models
With an eye toward understanding complexity control in deep learning, we study how infinitesimal regularization or gradient descent optimization lead to margin maximizing solutions in both homogeneous and non-homogeneous models, extending previous work that focused on infinitesimal regularization only in homogeneous models.
Solving a Class of Non-Convex Min-Max Games Using Iterative First Order Methods
In this paper, we study the problem in the non-convex regime and show that an \varepsilon--first order stationary point of the game can be computed when one of the player's objective can be optimized to global optimality efficiently.
Solving Non-Convex Non-Concave Min-Max Games Under Polyak-Łojasiewicz Condition
In this short note, we consider the problem of solving a min-max zero-sum game.
Provably Correct Automatic Sub-Differentiation for Qualified Programs
The \emph{Cheap Gradient Principle}~\citep{Griewank:2008:EDP:1455489} --- the computational cost of computing a $d$-dimensional vector of partial derivatives of a scalar function is nearly the same (often within a factor of $5$) as that of simply computing the scalar function itself --- is of central importance in optimization; it allows us to quickly obtain (high-dimensional) gradients of scalar loss functions which are subsequently used in black box gradient-based optimization procedures.
Gradient Descent Finds Global Minima of Deep Neural Networks
Gradient descent finds a global minimum in training deep neural networks despite the objective function being non-convex.
Regularization Matters: Generalization and Optimization of Neural Nets v.s. their Induced Kernel
We prove that for infinite-width two-layer nets, noisy gradient descent optimizes the regularized neural net loss to a global minimum in polynomial iterations.
Provably Correct Automatic Subdifferentiation for Qualified Programs
The Cheap Gradient Principle (Griewank 2008) --- the computational cost of computing the gradient of a scalar-valued function is nearly the same (often within a factor of $5$) as that of simply computing the function itself --- is of central importance in optimization; it allows us to quickly obtain (high dimensional) gradients of scalar loss functions which are subsequently used in black box gradient-based optimization procedures.
Algorithmic Regularization in Learning Deep Homogeneous Models: Layers are Automatically Balanced
Using a discretization argument, we analyze gradient descent with positive step size for the non-convex low-rank asymmetric matrix factorization problem without any regularization.
Adding One Neuron Can Eliminate All Bad Local Minima
One of the main difficulties in analyzing neural networks is the non-convexity of the loss function which may have many bad local minima.
Stochastic subgradient method converges on tame functions
This work considers the question: what convergence guarantees does the stochastic subgradient method have in the absence of smoothness and convexity?
Convergence of Gradient Descent on Separable Data
We show that for a large family of super-polynomial tailed losses, gradient descent iterates on linear networks of any depth converge in the direction of $L_2$ maximum-margin solution, while this does not hold for losses with heavier tails.
On the Power of Over-parametrization in Neural Networks with Quadratic Activation
We provide new theoretical insights on why over-parametrization is effective in learning neural networks.
On the Convergence and Robustness of Training GANs with Regularized Optimal Transport
A popular GAN formulation is based on the use of Wasserstein distance as a metric between probability distributions.
Better Generalization by Efficient Trust Region Method
Solving this subproblem is non-trivial---existing methods have only sub-linear convergence rate.
No Spurious Local Minima in a Two Hidden Unit ReLU Network
Deep learning models can be efficiently optimized via stochastic gradient descent, but there is little theoretical evidence to support this.
Gradient Descent Learns One-hidden-layer CNN: Don't be Afraid of Spurious Local Minima
We consider the problem of learning a one-hidden-layer neural network with non-overlapping convolutional layer and ReLU activation, i. e., $f(\mathbf{Z}, \mathbf{w}, \mathbf{a}) = \sum_j a_j\sigma(\mathbf{w}^T\mathbf{Z}_j)$, in which both the convolutional weights $\mathbf{w}$ and the output weights $\mathbf{a}$ are parameters to be learned.
Learning One-hidden-layer Neural Networks with Landscape Design
All global minima of $G$ correspond to the ground truth parameters.
First-order Methods Almost Always Avoid Saddle Points
We establish that first-order methods avoid saddle points for almost all initializations.
When is a Convolutional Filter Easy To Learn?
We show that (stochastic) gradient descent with random initialization can learn the convolutional filter in polynomial time and the convergence rate depends on the smoothness of the input distribution and the closeness of patches.
An inexact subsampled proximal Newton-type method for large-scale machine learning
We propose a fast proximal Newton-type algorithm for minimizing regularized finite sums that returns an $\epsilon$-suboptimal point in $\tilde{\mathcal{O}}(d(n + \sqrt{\kappa d})\log(\frac{1}{\epsilon}))$ FLOPS, where $n$ is number of samples, $d$ is feature dimension, and $\kappa$ is the condition number.
Theoretical insights into the optimization landscape of over-parameterized shallow neural networks
In this paper we study the problem of learning a shallow artificial neural network that best fits a training data set.
Gradient Descent Can Take Exponential Time to Escape Saddle Points
Although gradient descent (GD) almost always escapes saddle points asymptotically [Lee et al., 2016], this paper shows that even with fairly natural random initialization schemes and non-pathological functions, GD can be significantly slowed down by saddle points, taking exponential time to escape.
A Flexible Framework for Hypothesis Testing in High-dimensions
By duality between hypotheses testing and confidence intervals, the proposed framework can be used to obtain valid confidence intervals for various functionals of the model parameters.
Statistical Inference for Model Parameters in Stochastic Gradient Descent
Second, for high-dimensional linear regression, using a variant of the SGD algorithm, we construct a debiased estimator of each regression coefficient that is asymptotically normal.
Black-box Importance Sampling
Importance sampling is widely used in machine learning and statistics, but its power is limited by the restriction of using simple proposals for which the importance weights can be tractably calculated.
Sketching Meets Random Projection in the Dual: A Provable Recovery Algorithm for Big and High-dimensional Data
Sketching techniques have become popular for scaling up machine learning algorithms by reducing the sample size or dimensionality of massive data sets, while still maintaining the statistical power of big data.
Communication-Efficient Distributed Statistical Inference
CSL provides a communication-efficient surrogate to the global likelihood that can be used for low-dimensional estimation, high-dimensional regularized estimation and Bayesian inference.
Matrix Completion has No Spurious Local Minimum
Matrix completion is a basic machine learning problem that has wide applications, especially in collaborative filtering and recommender systems.
Gradient Descent Converges to Minimizers
We show that gradient descent converges to a local minimizer, almost surely with random initialization.
A Kernelized Stein Discrepancy for Goodness-of-fit Tests and Model Evaluation
We derive a new discrepancy statistic for measuring differences between two probability distributions based on combining Stein's identity with the reproducing kernel Hilbert space theory.
Evaluating the statistical significance of biclusters
Biclustering (also known as submatrix localization) is a problem of high practical relevance in exploratory analysis of high-dimensional data.
Learning Halfspaces and Neural Networks with Random Initialization
For loss functions that are $L$-Lipschitz continuous, we present algorithms to learn halfspaces and multi-layer neural networks that achieve arbitrarily small excess risk $\epsilon>0$.
$\ell_1$-regularized Neural Networks are Improperly Learnable in Polynomial Time
The sample complexity and the time complexity of the presented method are polynomial in the input dimension and in $(1/\epsilon,\log(1/\delta), F(k, L))$, where $F(k, L)$ is a function depending on $(k, L)$ and on the activation function, independent of the number of neurons.
Distributed Stochastic Variance Reduced Gradient Methods and A Lower Bound for Communication Complexity
We also prove a lower bound for the number of rounds of communication for a broad class of distributed first-order methods including the proposed algorithms in this paper.
Selective Inference and Learning Mixed Graphical Models
We present the Condition-on-Selection method that allows for valid selective inference, and study its application to the lasso, and several other selection algorithms.
Communication-efficient sparse regression: a one-shot approach
We devise a one-shot approach to distributed sparse regression in the high-dimensional setting.
Scalable methods for nonnegative matrix factorizations of near-separable tall-and-skinny matrices
We demonstrate the efficacy of these algorithms on terabyte-sized synthetic matrices and real-world matrices from scientific computing and bioinformatics.
Exact Post Model Selection Inference for Marginal Screening
We develop a framework for post model selection inference, via marginal screening, in linear regression.
On model selection consistency of penalized M-estimators: a geometric theory
Penalized M-estimators are used in diverse areas of science and engineering to fit high-dimensional models with some low-dimensional structure.
Using Multiple Samples to Learn Mixture Models
In the mixture models problem it is assumed that there are $K$ distributions $\theta_{1},\ldots,\theta_{K}$ and one gets to observe a sample from a mixture of these distributions with unknown coefficients.
Exact post-selection inference, with application to the lasso
We develop a general approach to valid inference after model selection.
On model selection consistency of regularized M-estimators
Regularized M-estimators are used in diverse areas of science and engineering to fit high-dimensional models with some low-dimensional structure.
Proximal Newton-type methods for minimizing composite functions
We generalize Newton-type methods for minimizing smooth functions to handle a sum of two convex functions: a smooth function and a nonsmooth function with a simple proximal mapping.
Learning Mixed Graphical Models
We present a new pairwise model for graphical models with both continuous and discrete variables that is amenable to structure learning.
Practical Large-Scale Optimization for Max-norm Regularization
The max-norm was proposed as a convex matrix regularizer by Srebro et al (2004) and was shown to be empirically superior to the trace-norm for collaborative filtering problems.
