arXiv subjects

Chirag Gupta

Publications and source records attributed to Chirag Gupta.

24 records · Page 2Linked to original sources

arXiv2022

Distribution-free binary classification: prediction sets, confidence intervals and calibration

We study three notions of uncertainty quantification -- calibration, confidence intervals and prediction sets -- for binary classification in the distribution-free setting, that is without making any distributional assumptions on the data. With a focus towards calibration, we establish a 'tripod' of theorems that connect these three notions for score-based classifiers. A direct implication is that distribution-free calibration is only possible, even asymptotically, using a scoring function whose level sets partition the feature space into at most countably many sets. Parametric calibration schemes such as variants of Platt scaling do not satisfy this requirement, while nonparametric schemes based on binning do. To close the loop, we derive distribution-free confidence intervals for binned probabilities for both fixed-width and uniform-mass binning. As a consequence of our 'tripod' theorems, these confidence intervals for binned probabilities lead to distribution-free calibration. We also derive extensions to settings with streaming data and covariate shift.

stat.ML↗

arXiv2021

Distribution-free calibration guarantees for histogram binning without sample splitting

We prove calibration guarantees for the popular histogram binning (also called uniform-mass binning) method of Zadrozny and Elkan [2001]. Histogram binning has displayed strong practical performance, but theoretical guarantees have only been shown for sample split versions that avoid 'double dipping' the data. We demonstrate that the statistical cost of sample splitting is practically significant on a credit default dataset. We then prove calibration guarantees for the original method that double dips the data, using a certain Markov property of order statistics. Based on our results, we make practical recommendations for choosing the number of bins in histogram binning. In our illustrative simulations, we propose a new tool for assessing calibration -- validity plots -- which provide more information than an ECE estimate. Code for this work will be made publicly available at https://github.com/aigen/df-posthoc-calibration.

stat.ME↗

arXiv2021

Path Length Bounds for Gradient Descent and Flow

We derive bounds on the path length $ζ$ of gradient descent (GD) and gradient flow (GF) curves for various classes of smooth convex and nonconvex functions. Among other results, we prove that: (a) if the iterates are linearly convergent with factor $(1-c)$, then $ζ$ is at most $\mathcal{O}(1/c)$; (b) under the Polyak-Kurdyka-Lojasiewicz (PKL) condition, $ζ$ is at most $\mathcal{O}(\sqrtκ)$, where $κ$ is the condition number, and at least $\widetildeΩ(\sqrt{d} \wedge κ^{1/4})$; (c) for quadratics, $ζ$ is $Θ(\min\{\sqrt{d},\sqrt{\log κ}\})$ and in some cases can be independent of $κ$; (d) assuming just convexity, $ζ$ can be at most $2^{4d\log d}$; (e) for separable quasiconvex functions, $ζ$ is $Θ(\sqrt{d})$. Thus, we advance current understanding of the properties of GD and GF curves beyond rates of convergence. We expect our techniques to facilitate future studies for other algorithms.

cs.LG↗

arXiv2021

Modern Machine and Deep Learning Systems as a way to achieve Man-Computer Symbiosis

Man-Computer Symbiosis (MCS) was originally envisioned by the famous computer pioneer J.C.R. Licklider in 1960, as a logical evolution of the then inchoate relationship between computer and humans. In his paper, Licklider provided a set of criteria by which to judge if a Man-Computer System is a symbiotic one, and also provided some predictions about such systems in the near and far future. Since then, innovations in computer networks and the invention of the Internet were major developments towards that end. However, with most systems based on conventional logical algorithms, many aspects of Licklider's MCS remained unfulfilled. This paper explores the extent to which modern machine learning systems in general, and deep learning ones in particular best exemplify MCS systems, and why they are the prime contenders to achieve a true Man-Computer Symbiosis as described by Licklider in his original paper in the future. The case for deep learning is built by illustrating each point of the original criteria as well as the criteria laid by subsequent research into MCS systems, with specific examples and applications provided to strengthen the arguments. The efficacy of deep neural networks in achieving Artificial General Intelligence, which would be the perfect version of an MCS system is also explored.

cs.LG↗

arXiv2020

Shallow Encoder Deep Decoder (SEDD) Networks for Image Encryption and Decryption

This paper explores a new framework for lossy image encryption and decryption using a simple shallow encoder neural network E for encryption, and a complex deep decoder neural network D for decryption. E is kept simple so that encoding can be done on low power and portable devices and can in principle be any nonlinear function which outputs an encoded vector. D is trained to decode the encodings using the dataset of image - encoded vector pairs obtained from E and happens independently of E. As the encodings come from E which while being a simple neural network, still has thousands of random parameters and therefore the encodings would be practically impossible to crack without D. This approach differs from autoencoders as D is trained completely independently of E, although the structure may seem similar. Therefore, this paper also explores empirically if a deep neural network can learn to reconstruct the original data in any useful form given the output of a neural network or any other nonlinear function, which can have very useful applications in Cryptanalysis. Experiments demonstrate the potential of the framework through qualitative and quantitative evaluation of the decoded images from D along with some limitations.

cs.LG↗

arXiv2020

Self learning robot using real-time neural networks

With the advancements in high volume, low precision computational technology and applied research on cognitive artificially intelligent heuristic systems, machine learning solutions through neural networks with real-time learning has seen an immense interest in the research community as well the industry. This paper involves research, development and experimental analysis of a neural network implemented on a robot with an arm through which evolves to learn to walk in a straight line or as required. The neural network learns using the algorithms of Gradient Descent and Backpropagation. Both the implementation and training of the neural network is done locally on the robot on a raspberry pi 3 so that its learning process is completely independent. The neural network is first tested on a custom simulator developed on MATLAB and then implemented on the raspberry computer. Data at each generation of the evolving network is stored, and analysis both mathematical and graphical is done on the data. Impact of factors like the learning rate and error tolerance on the learning process and final output is analyzed.

cs.RO↗