Search Results for author: Praneeth Netrapalli

Found 66 papers, 14 papers with code

Near Optimal Heteroscedastic Regression with Symbiotic Learning

no code implementations25 Jun 2023 Dheeraj Baby, Aniket Das, Dheeraj Nagaraj, Praneeth Netrapalli

Our work shows that we can estimate $\mathbf{w}^{*}$ in squared norm up to an error of $\tilde{O}\left(\|\mathbf{f}^{*}\|^2 \cdot \left(\frac{1}{n} + \left(\frac{d}{n}\right)^2\right)\right)$ and prove a matching lower bound (upto log factors).

Econometrics regression +2

Simplicity Bias in 1-Hidden Layer Neural Networks

no code implementations1 Feb 2023 Depen Morwani, Jatin Batra, Prateek Jain, Praneeth Netrapalli

More concretely, (i) we define SB as the network essentially being a function of a low dimensional projection of the inputs (ii) theoretically, we show that when the data is linearly separable, the network primarily depends on only the linearly separable ($1$-dimensional) subspace even in the presence of an arbitrarily large number of other, more complex features which could have led to a significantly more robust classifier, (iii) empirically, we show that models trained on real datasets such as Imagenette and Waterbirds-Landbirds indeed depend on a low dimensional projection of the inputs, thereby demonstrating SB on these datasets, iv) finally, we present a natural ensemble approach that encourages diversity in models by training successive models on features not used by earlier models, and demonstrate that it yields models that are significantly more robust to Gaussian noise.

Consistent Multiclass Algorithms for Complex Metrics and Constraints

1 code implementation18 Oct 2022 Harikrishna Narasimhan, Harish G. Ramaswamy, Shiv Kumar Tavker, Drona Khurana, Praneeth Netrapalli, Shivani Agarwal

We present consistent algorithms for multiclass learning with complex performance metrics and constraints, where the objective and constraints are defined by arbitrary functions of the confusion matrix.


Learning an Invertible Output Mapping Can Mitigate Simplicity Bias in Neural Networks

no code implementations4 Oct 2022 Sravanti Addepalli, Anshul Nasery, R. Venkatesh Babu, Praneeth Netrapalli, Prateek Jain

To bridge the gap between these two lines of work, we first hypothesize and verify that while SB may not altogether preclude learning complex features, it amplifies simpler features over complex ones.

Optimistic MLE -- A Generic Model-based Algorithm for Partially Observable Sequential Decision Making

no code implementations29 Sep 2022 Qinghua Liu, Praneeth Netrapalli, Csaba Szepesvári, Chi Jin

We prove that OMLE learns the near-optimal policies of an enormously rich class of sequential decision making problems in a polynomial number of samples.

Decision Making Model-based Reinforcement Learning +1

DAFT: Distilling Adversarially Fine-tuned Models for Better OOD Generalization

no code implementations19 Aug 2022 Anshul Nasery, Sravanti Addepalli, Praneeth Netrapalli, Prateek Jain

We consider the problem of OOD generalization, where the goal is to train a model that performs well on test distributions that are different from the training distribution.

MET: Masked Encoding for Tabular Data

no code implementations17 Jun 2022 Kushal Majmundar, Sachin Goyal, Praneeth Netrapalli, Prateek Jain

Typical contrastive learning based SSL methods require instance-wise data augmentations which are difficult to design for unstructured tabular data.

Contrastive Learning Representation Learning

All Mistakes Are Not Equal: Comprehensive Hierarchy Aware Multi-label Predictions (CHAMP)

no code implementations17 Jun 2022 Ashwin Vaswani, Gaurav Aggarwal, Praneeth Netrapalli, Narayan G Hegde

Compared to standard multilabel baselines, CHAMP provides improved AUPRC in both robustness (8. 87% mean percentage improvement ) and less data regimes.

Classification Hierarchical Multi-label Classification

Statistically and Computationally Efficient Linear Meta-representation Learning

no code implementations NeurIPS 2021 Kiran K. Thekumparampil, Prateek Jain, Praneeth Netrapalli, Sewoong Oh

To cope with such data scarcity, meta-representation learning methods train across many related tasks to find a shared (lower-dimensional) representation of the data where all tasks can be solved accurately.

Few-Shot Learning Representation Learning

Online Target Q-learning with Reverse Experience Replay: Efficiently finding the Optimal Policy for Linear MDPs

no code implementations ICLR 2022 Naman Agarwal, Syomantak Chaudhuri, Prateek Jain, Dheeraj Nagaraj, Praneeth Netrapalli

The starting point of our work is the observation that in practice, Q-learning is used with two important modifications: (i) training with two networks, called online network and target network simultaneously (online target learning, or OTL) , and (ii) experience replay (ER) (Mnih et al., 2015).

Q-Learning Reinforcement Learning (RL)

Minimax Optimization with Smooth Algorithmic Adversaries

1 code implementation ICLR 2022 Tanner Fiez, Chi Jin, Praneeth Netrapalli, Lillian J. Ratliff

This paper considers minimax optimization $\min_x \max_y f(x, y)$ in the challenging setting where $f$ can be both nonconvex in $x$ and nonconcave in $y$.

Near-optimal Offline and Streaming Algorithms for Learning Non-Linear Dynamical Systems

no code implementations NeurIPS 2021 Prateek Jain, Suhas S Kowshik, Dheeraj Nagaraj, Praneeth Netrapalli

In this work, we improve existing results for learning nonlinear systems in a number of ways: a) we provide the first offline algorithm that can learn non-linear dynamical systems without the mixing assumption, b) we significantly improve upon the sample complexity of existing results for mixing systems, c) in the much harder one-pass, streaming setting we study a SGD with Reverse Experience Replay ($\mathsf{SGD-RER}$) method, and demonstrate that for mixing systems, it achieves the same sample complexity as our offline algorithm, d) we justify the expansivity assumption by showing that for the popular ReLU link function -- a non-expansive but easy to learn link function with i. i. d.

Sample Efficient Linear Meta-Learning by Alternating Minimization

no code implementations18 May 2021 Kiran Koshy Thekumparampil, Prateek Jain, Praneeth Netrapalli, Sewoong Oh

We show that, for a constant subspace dimension MLLAM obtains nearly-optimal estimation error, despite requiring only $\Omega(\log d)$ samples per task.


Streaming Linear System Identification with Reverse Experience Replay

no code implementations NeurIPS 2021 Prateek Jain, Suhas S Kowshik, Dheeraj Nagaraj, Praneeth Netrapalli

Thus, we provide the first -- to the best of our knowledge -- optimal SGD-style algorithm for the classical problem of linear system identification with a first order oracle.

Reinforcement Learning (RL) Time Series Analysis

Do Input Gradients Highlight Discriminative Features?

1 code implementation NeurIPS 2021 Harshay Shah, Prateek Jain, Praneeth Netrapalli

We believe that the DiffROAR evaluation framework and BlockMNIST-based datasets can serve as sanity checks to audit instance-specific interpretability methods; code and data available at https://github. com/harshays/inputgradients.

Image Classification

Optimal Regret Algorithm for Pseudo-1d Bandit Convex Optimization

no code implementations15 Feb 2021 Aadirupa Saha, Nagarajan Natarajan, Praneeth Netrapalli, Prateek Jain

We study online learning with bandit feedback (i. e. learner has access to only zeroth-order oracle) where cost/reward functions $\f_t$ admit a "pseudo-1d" structure, i. e. $\f_t(\w) = \loss_t(\pred_t(\w))$ where the output of $\pred_t$ is one-dimensional.

Decision Making

Projection Efficient Subgradient Method and Optimal Nonsmooth Frank-Wolfe Method

no code implementations NeurIPS 2020 Kiran Koshy Thekumparampil, Prateek Jain, Praneeth Netrapalli, Sewoong Oh

Further, instead of a PO if we only have a linear minimization oracle (LMO, a la Frank-Wolfe) to access the constraint set, an extension of our method, MOLES, finds a feasible $\epsilon$-suboptimal solution using $O(\epsilon^{-2})$ LMO calls and FO calls---both match known lower bounds, resolving a question left open since White (1993).

Learning Minimax Estimators via Online Learning

no code implementations19 Jun 2020 Kartik Gupta, Arun Sai Suggala, Adarsh Prasad, Praneeth Netrapalli, Pradeep Ravikumar

We view the problem of designing minimax estimators as finding a mixed strategy Nash equilibrium of a zero-sum game.

Least Squares Regression with Markovian Data: Fundamental Limits and Algorithms

no code implementations NeurIPS 2020 Guy Bresler, Prateek Jain, Dheeraj Nagaraj, Praneeth Netrapalli, Xian Wu

Our improved rate serves as one of the first results where an algorithm outperforms SGD-DD on an interesting Markov chain and also provides one of the first theoretical analyses to support the use of experience replay in practice.


The Pitfalls of Simplicity Bias in Neural Networks

2 code implementations NeurIPS 2020 Harshay Shah, Kaustav Tamuly, aditi raghunathan, Prateek Jain, Praneeth Netrapalli

Furthermore, previous settings that use SB to theoretically justify why neural networks generalize well do not simultaneously capture the non-robustness of neural networks---a widely observed phenomenon in practice [Goodfellow et al. 2014, Jo and Bengio 2017].

Follow the Perturbed Leader: Optimism and Fast Parallel Algorithms for Smooth Minimax Games

no code implementations NeurIPS 2020 Arun Sai Suggala, Praneeth Netrapalli

For Lipschitz and smooth nonconvex-nonconcave games, our algorithm requires access to an optimization oracle which computes the perturbed best response.

P-SIF: Document Embeddings Using Partition Averaging

1 code implementation18 May 2020 Vivek Gupta, Ankit Saw, Pegah Nokhiz, Praneeth Netrapalli, Piyush Rai, Partha Talukdar

One of the key reasons is that a longer document is likely to contain words from many different topics; hence, creating a single vector while ignoring all the topical structure is unlikely to yield an effective document representation.

Non-Gaussianity of Stochastic Gradient Noise

no code implementations21 Oct 2019 Abhishek Panigrahi, Raghav Somani, Navin Goyal, Praneeth Netrapalli

What enables Stochastic Gradient Descent (SGD) to achieve better generalization than Gradient Descent (GD) in Neural Network training?

Efficient Algorithms for Smooth Minimax Optimization

2 code implementations NeurIPS 2019 Kiran Koshy Thekumparampil, Prateek Jain, Praneeth Netrapalli, Sewoong Oh

This paper studies first order methods for solving smooth minimax optimization problems $\min_x \max_y g(x, y)$ where $g(\cdot,\cdot)$ is smooth and $g(x,\cdot)$ is concave for each $x$.

Universality Patterns in the Training of Neural Networks

no code implementations17 May 2019 Raghav Somani, Navin Goyal, Prateek Jain, Praneeth Netrapalli

This paper proposes and demonstrates a surprising pattern in the training of neural networks: there is a one to one relation between the values of any pair of losses (such as cross entropy, mean squared error, 0/1 error etc.)

Rethinking learning rate schedules for stochastic optimization

no code implementations ICLR 2019 Rong Ge, Sham M. Kakade, Rahul Kidambi, Praneeth Netrapalli

One plausible explanation is that non-convex neural network training procedures are better suited to the use of fundamentally different learning rate schedules, such as the ``cut the learning rate every constant number of epochs'' method (which more closely resembles an exponentially decaying learning rate schedule); note that this widely used schedule is in stark contrast to the polynomial decay schemes prescribed in the stochastic approximation literature, which are indeed shown to be (worst case) optimal for classes of convex optimization problems.

Stochastic Optimization

Making the Last Iterate of SGD Information Theoretically Optimal

no code implementations29 Apr 2019 Prateek Jain, Dheeraj Nagaraj, Praneeth Netrapalli

While classical theoretical analysis of SGD for convex problems studies (suffix) \emph{averages} of iterates and obtains information theoretically optimal bounds on suboptimality, the \emph{last point} of SGD is, by far, the most preferred choice in practice.

The Step Decay Schedule: A Near Optimal, Geometrically Decaying Learning Rate Procedure For Least Squares

1 code implementation NeurIPS 2019 Rong Ge, Sham M. Kakade, Rahul Kidambi, Praneeth Netrapalli

First, this work shows that even if the time horizon T (i. e. the number of iterations SGD is run for) is known in advance, SGD's final iterate behavior with any polynomially decaying learning rate scheme is highly sub-optimal compared to the minimax rate (by a condition number factor in the strongly convex case and a factor of $\sqrt{T}$ in the non-strongly convex case).

Stochastic Optimization

Online Non-Convex Learning: Following the Perturbed Leader is Optimal

no code implementations19 Mar 2019 Arun Sai Suggala, Praneeth Netrapalli

We show that the classical Follow the Perturbed Leader (FTPL) algorithm achieves optimal regret rate of $O(T^{-1/2})$ in this setting.

SGD without Replacement: Sharper Rates for General Smooth Convex Functions

no code implementations4 Mar 2019 Prateek Jain, Dheeraj Nagaraj, Praneeth Netrapalli

For {\em small} $K$, we show \sgdwor can achieve same convergence rate as \sgd for {\em general smooth strongly-convex} functions.

On Nonconvex Optimization for Machine Learning: Gradients, Stochasticity, and Saddle Points

no code implementations13 Feb 2019 Chi Jin, Praneeth Netrapalli, Rong Ge, Sham M. Kakade, Michael. I. Jordan

More recent theory has shown that GD and SGD can avoid saddle points, but the dependence on dimension in these analyses is polynomial.

BIG-bench Machine Learning

A Short Note on Concentration Inequalities for Random Vectors with SubGaussian Norm

no code implementations11 Feb 2019 Chi Jin, Praneeth Netrapalli, Rong Ge, Sham M. Kakade, Michael. I. Jordan

In this note, we derive concentration inequalities for random vectors with subGaussian norm (a generalization of both subGaussian random vectors and norm bounded random vectors), which are tight up to logarithmic factors.

What is Local Optimality in Nonconvex-Nonconcave Minimax Optimization?

1 code implementation ICML 2020 Chi Jin, Praneeth Netrapalli, Michael. I. Jordan

Minimax optimization has found extensive applications in modern machine learning, in settings such as generative adversarial networks (GANs), adversarial training and multi-agent reinforcement learning.

BIG-bench Machine Learning Multi-agent Reinforcement Learning

Support Recovery for Orthogonal Matching Pursuit: Upper and Lower bounds

no code implementations NeurIPS 2018 Raghav Somani, Chirag Gupta, Prateek Jain, Praneeth Netrapalli

This paper studies the problem of sparse regression where the goal is to learn a sparse vector that best optimizes a given objective function.

Generalization Bounds regression

Unsupervised Document Representation using Partition Word-Vectors Averaging

no code implementations27 Sep 2018 Vivek Gupta, Ankit Kumar Saw, Partha Pratim Talukdar, Praneeth Netrapalli

One reason for this degradation is due to the fact that a longer document is likely to contain words from many different themes (or topics), and hence creating a single vector while ignoring all the thematic structure is unlikely to yield an effective representation of the document.

Document Classification

Learnability of Learned Neural Networks

no code implementations ICLR 2018 Rahul Anand Sharma, Navin Goyal, Monojit Choudhury, Praneeth Netrapalli

This paper explores the simplicity of learned neural networks under various settings: learned on real vs random data, varying size/architecture and using large minibatch size vs small minibatch size.

Accelerated Gradient Descent Escapes Saddle Points Faster than Gradient Descent

no code implementations28 Nov 2017 Chi Jin, Praneeth Netrapalli, Michael. I. Jordan

Nesterov's accelerated gradient descent (AGD), an instance of the general family of "momentum methods", provably achieves faster convergence rate than gradient descent (GD) in the convex setting.

Leverage Score Sampling for Faster Accelerated Regression and ERM

no code implementations22 Nov 2017 Naman Agarwal, Sham Kakade, Rahul Kidambi, Yin Tat Lee, Praneeth Netrapalli, Aaron Sidford

Given a matrix $\mathbf{A}\in\mathbb{R}^{n\times d}$ and a vector $b \in\mathbb{R}^{d}$, we show how to compute an $\epsilon$-approximate solution to the regression problem $ \min_{x\in\mathbb{R}^{d}}\frac{1}{2} \|\mathbf{A} x - b\|_{2}^{2} $ in time $ \tilde{O} ((n+\sqrt{d\cdot\kappa_{\text{sum}}})\cdot s\cdot\log\epsilon^{-1}) $ where $\kappa_{\text{sum}}=\mathrm{tr}\left(\mathbf{A}^{\top}\mathbf{A}\right)/\lambda_{\min}(\mathbf{A}^{T}\mathbf{A})$ and $s$ is the maximum number of non-zero entries in a row of $\mathbf{A}$.


A Markov Chain Theory Approach to Characterizing the Minimax Optimality of Stochastic Gradient Descent (for Least Squares)

no code implementations25 Oct 2017 Prateek Jain, Sham M. Kakade, Rahul Kidambi, Praneeth Netrapalli, Venkata Krishna Pillutla, Aaron Sidford

This work provides a simplified proof of the statistical minimax optimality of (iterate averaged) stochastic gradient descent (SGD), for the special case of least squares.

Accelerating Stochastic Gradient Descent For Least Squares Regression

no code implementations26 Apr 2017 Prateek Jain, Sham M. Kakade, Rahul Kidambi, Praneeth Netrapalli, Aaron Sidford

There is widespread sentiment that it is not possible to effectively utilize fast gradient methods (e. g. Nesterov's acceleration, conjugate gradient, heavy ball) for the purposes of stochastic optimization due to their instability and error accumulation, a notion made precise in d'Aspremont 2008 and Devolder, Glineur, and Nesterov 2014.

regression Stochastic Optimization

Spectrum Approximation Beyond Fast Matrix Multiplication: Algorithms and Hardness

no code implementations13 Apr 2017 Cameron Musco, Praneeth Netrapalli, Aaron Sidford, Shashanka Ubaru, David P. Woodruff

We thus effectively compute a histogram of the spectrum, which can stand in for the true singular values in many applications.

How to Escape Saddle Points Efficiently

no code implementations ICML 2017 Chi Jin, Rong Ge, Praneeth Netrapalli, Sham M. Kakade, Michael. I. Jordan

This paper shows that a perturbed form of gradient descent converges to a second-order stationary point in a number iterations which depends only poly-logarithmically on dimension (i. e., it is almost "dimension-free").

Thresholding based Efficient Outlier Robust PCA

no code implementations18 Feb 2017 Yeshwanth Cherapanamjeri, Prateek Jain, Praneeth Netrapalli

That is, given a data matrix $M^*$, where $(1-\alpha)$ fraction of the points are noisy samples from a low-dimensional subspace while $\alpha$ fraction of the points can be arbitrary outliers, the goal is to recover the subspace accurately.

Parallelizing Stochastic Gradient Descent for Least Squares Regression: mini-batching, averaging, and model misspecification

1 code implementation12 Oct 2016 Prateek Jain, Sham M. Kakade, Rahul Kidambi, Praneeth Netrapalli, Aaron Sidford

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 estimate and for parallelizing SGD and (2) tail-averaging, a method involving averaging the final few iterates of SGD to decrease the variance in SGD's final iterate.


Provable Efficient Online Matrix Completion via Non-convex Stochastic Gradient Descent

no code implementations NeurIPS 2016 Chi Jin, Sham M. Kakade, Praneeth Netrapalli

While existing algorithms are efficient for the offline setting, they could be highly inefficient for the online setting.

Matrix Completion

Faster Eigenvector Computation via Shift-and-Invert Preconditioning

no code implementations26 May 2016 Dan Garber, Elad Hazan, Chi Jin, Sham M. Kakade, Cameron Musco, Praneeth Netrapalli, Aaron Sidford

We give faster algorithms and improved sample complexities for estimating the top eigenvector of a matrix $\Sigma$ -- i. e. computing a unit vector $x$ such that $x^T \Sigma x \ge (1-\epsilon)\lambda_1(\Sigma)$: Offline Eigenvector Estimation: Given an explicit $A \in \mathbb{R}^{n \times d}$ with $\Sigma = A^TA$, we show how to compute an $\epsilon$ approximate top eigenvector in time $\tilde O([nnz(A) + \frac{d*sr(A)}{gap^2} ]* \log 1/\epsilon )$ and $\tilde O([\frac{nnz(A)^{3/4} (d*sr(A))^{1/4}}{\sqrt{gap}} ] * \log 1/\epsilon )$.

Stochastic Optimization

Robust Shift-and-Invert Preconditioning: Faster and More Sample Efficient Algorithms for Eigenvector Computation

no code implementations29 Oct 2015 Chi Jin, Sham M. Kakade, Cameron Musco, Praneeth Netrapalli, Aaron Sidford

Combining our algorithm with previous work to initialize $x_0$, we obtain a number of improved sample complexity and runtime results.

Stochastic Optimization

Learning Planar Ising Models

no code implementations3 Feb 2015 Jason K. Johnson, Diane Oyen, Michael Chertkov, Praneeth Netrapalli

Inference and learning of graphical models are both well-studied problems in statistics and machine learning that have found many applications in science and engineering.

Fast Exact Matrix Completion with Finite Samples

no code implementations4 Nov 2014 Prateek Jain, Praneeth Netrapalli

In this paper, we present a fast iterative algorithm that solves the matrix completion problem by observing $O(nr^5 \log^3 n)$ entries, which is independent of the condition number and the desired accuracy.

Matrix Completion

Non-convex Robust PCA

no code implementations NeurIPS 2014 Praneeth Netrapalli, U. N. Niranjan, Sujay Sanghavi, Animashree Anandkumar, Prateek Jain

In contrast, existing methods for robust PCA, which are based on convex optimization, have $O(m^2n)$ complexity per iteration, and take $O(1/\epsilon)$ iterations, i. e., exponentially more iterations for the same accuracy.

Learning Sparsely Used Overcomplete Dictionaries via Alternating Minimization

no code implementations30 Oct 2013 Alekh Agarwal, Animashree Anandkumar, Prateek Jain, Praneeth Netrapalli

Alternating minimization is a popular heuristic for sparse coding, where the dictionary and the coefficients are estimated in alternate steps, keeping the other fixed.

A Clustering Approach to Learn Sparsely-Used Overcomplete Dictionaries

no code implementations8 Sep 2013 Alekh Agarwal, Animashree Anandkumar, Praneeth Netrapalli

We consider the problem of learning overcomplete dictionaries in the context of sparse coding, where each sample selects a sparse subset of dictionary elements.

Clustering regression

Phase Retrieval using Alternating Minimization

1 code implementation NeurIPS 2013 Praneeth Netrapalli, Prateek Jain, Sujay Sanghavi

Empirically, we demonstrate that alternating minimization performs similar to recently proposed convex techniques for this problem (which are based on "lifting" to a convex matrix problem) in sample complexity and robustness to noise.


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