Naresh Manwani

Siddharth Shrivastava, Mahvith Akshintala, B Vamsha Vardhan Reddy et al.

Strategic classification studies settings in which agents respond to a deployed classifier by modifying observable features at a cost. Classical models typically treat such responses as cosmetic: features may change, but true labels remain fixed. We study an improvement-aware variant in which strategic responses can induce genuine changes in outcome-relevant features. Agents choose post-deployment feature vectors strategically, and labels are then generated according to a stable conditional outcome law that preserves the relationship between features and outcomes. We formalize this problem for linear classifiers under a single-index qualification model and linear-decomposable costs. We show that the strategic-optimal classifier is obtained by a parallel shift of the Bayes-optimal decision boundary, and that it provides a better surrogate for the improvement-aware objective than the Bayes classifier. Since improvement-aware learning requires post-deployment labels, which are typically unavailable before deployment, we provide PAC-style guar- antees under an oracle model, propose a practical plug-in algorithm, establish its generalization bound, and evaluate it on synthetic and real-world datasets.

Samartha S Maheshwara, Naresh Manwani

This paper presents a robust approach for learning from noisy pairwise comparisons. We propose sufficient conditions on the loss function under which the risk minimization framework becomes robust to noise in the pairwise similar dissimilar data. Our approach does not require the knowledge of noise rate in the uniform noise case. In the case of conditional noise, the proposed method depends on the noise rates. For such cases, we offer a provably correct approach for estimating the noise rates. Thus, we propose an end-to-end approach to learning robust classifiers in this setting. We experimentally show that the proposed approach RoLNiP outperforms the robust state-of-the-art methods for learning with noisy pairwise comparisons.

Naresh Manwani, Mudit Agarwal

In this paper, we present online algorithm called {\it Delaytron} for learning multi class classifiers using delayed bandit feedbacks. The sequence of feedback delays $\{d_t\}_{t=1}^T$ is unknown to the algorithm. At the $t$-th round, the algorithm observes an example $\mathbf{x}_t$ and predicts a label $\tilde{y}_t$ and receives the bandit feedback $\mathbb{I}[\tilde{y}_t=y_t]$ only $d_t$ rounds later. When $t+d_t>T$, we consider that the feedback for the $t$-th round is missing. We show that the proposed algorithm achieves regret of $\mathcal{O}\left(\sqrt{\frac{2 K}γ\left[\frac{T}{2}+\left(2+\frac{L^2}{R^2\Vert \W\Vert_F^2}\right)\sum_{t=1}^Td_t\right]}\right)$ when the loss for each missing sample is upper bounded by $L$. In the case when the loss for missing samples is not upper bounded, the regret achieved by Delaytron is $\mathcal{O}\left(\sqrt{\frac{2 K}γ\left[\frac{T}{2}+2\sum_{t=1}^Td_t+\vert \mathcal{M}\vert T\right]}\right)$ where $\mathcal{M}$ is the set of missing samples in $T$ rounds. These bounds were achieved with a constant step size which requires the knowledge of $T$ and $\sum_{t=1}^Td_t$. For the case when $T$ and $\sum_{t=1}^Td_t$ are unknown, we use a doubling trick for online learning and proposed Adaptive Delaytron. We show that Adaptive Delaytron achieves a regret bound of $\mathcal{O}\left(\sqrt{T+\sum_{t=1}^Td_t}\right)$. We show the effectiveness of our approach by experimenting on various datasets and comparing with state-of-the-art approaches.

Rishabh Bhattacharya, Vikaskumar Kalsariya, Naresh Manwani

Model merging has emerged as a powerful paradigm for combining the capabilities of distinct expert models without the high computational cost of retraining, yet current methods are fundamentally constrained to homogeneous architectures. For GNNs, however, message passing is topology-dependent and sensitive to misalignment, making direct parameter-space merging unreliable. To bridge this gap, we introduce H-GRAMA (Heterogeneous Graph Routing and Message Alignment), a training-free framework that lifts merging from parameter space to operator space. We formalize Universal Message Passing Mixture (UMPM), a shared operator family that expresses heterogeneous GNN layers in a common functional language. H-GRAMA enables cross-architecture GNN merging (e.g., GCN to GAT) without retraining, retaining high specialist accuracy in most cases in compatible depth settings and achieving inference speedups of 1.2x to 1.9x over ensembles.

Naresh Manwani, M Elamparithy, Tanish Taneja

In this paper, we introduce directional feedback in the ordinal regression setting, in which the learner receives feedback on whether the predicted label is on the left or the right side of the actual label. This is a weak supervision setting for ordinal regression compared to the full information setting, where the learner can access the labels. We propose an online algorithm for ordinal regression using directional feedback. The proposed algorithm uses an exploration-exploitation scheme to learn from directional feedback efficiently. Furthermore, we introduce its kernel-based variant to learn non-linear ordinal regression models in an online setting. We use a truncation trick to make the kernel implementation more memory efficient. The proposed algorithm maintains the ordering of the thresholds in the expected sense. Moreover, it achieves the expected regret of $\mathcal{O}(\log T)$. We compare our approach with a full information and a weakly supervised algorithm for ordinal regression on synthetic and real-world datasets. The proposed approach, which learns using directional feedback, performs comparably (sometimes better) to its full information counterpart.

Rishabh Bhattacharya, Naresh Manwani

Structural shifts pose a significant challenge for graph neural networks, as graph topology acts as a covariate that can vary across domains. Existing domain generalization methods rely on fixed structural augmentations or training on globally perturbed graphs, mechanisms that do not pinpoint which specific edges encode domain-invariant information. We argue that domain-invariant structural information is not rigidly tied to a single topology but resides in the consensus across multiple graph structures derived from topology and feature similarity. To capture this, we first propose EdgeMask-DG, a novel min-max algorithm where an edge masker learns to find worst-case continuous masks subject to a sparsity constraint, compelling a task GNN to perform effectively under these adversarial structural perturbations. Building upon this, we introduce EdgeMask-DG*, an extension that applies this adversarial masking principle to an enriched graph. This enriched graph combines the original topology with feature-derived edges, allowing the model to discover invariances even when the original topology is noisy or domain-specific. EdgeMask-DG* is the first to systematically combine adaptive adversarial topology search with feature-enriched graphs. We provide a formal justification for our approach from a robust optimization perspective. We demonstrate that EdgeMask-DG* achieves new state-of-the-art performance on diverse graph domain generalization benchmarks, including citation networks, social networks, and temporal graphs. Notably, on the Cora OOD benchmark, EdgeMask-DG* lifts the worst-case domain accuracy to 78.0\%, a +3.8 pp improvement over the prior state of the art (74.2\%). The source code for our experiments can be found here: https://anonymous.4open.science/r/TMLR-EAEF/

Uday Bhaskar, Rishabh Bhattacharya, Avinash Patel et al.

Foundation models, especially vision-language models (VLMs), offer compelling zero-shot object detection for applications like autonomous driving, a domain where manual labelling is prohibitively expensive. However, their detection latency and tendency to hallucinate predictions render them unsuitable for direct deployment. This work introduces a novel pipeline that addresses this challenge by leveraging VLMs to automatically generate pseudo-labels for training efficient, real-time object detectors. Our key innovation is a per-object co-teaching-based training strategy that mitigates the inherent noise in VLM-generated labels. The proposed per-object coteaching approach filters noisy bounding boxes from training instead of filtering the entire image. Specifically, two YOLO models learn collaboratively, filtering out unreliable boxes from each mini-batch based on their peers' per-object loss values. Overall, our pipeline provides an efficient, robust, and scalable approach to train high-performance object detectors for autonomous driving, significantly reducing reliance on costly human annotation. Experimental results on the KITTI dataset demonstrate that our method outperforms a baseline YOLOv5m model, achieving a significant mAP@0.5 boost ($31.12\%$ to $46.61\%$) while maintaining real-time detection latency. Furthermore, we show that supplementing our pseudo-labelled data with a small fraction of ground truth labels ($10\%$) leads to further performance gains, reaching $57.97\%$ mAP@0.5 on the KITTI dataset. We observe similar performance improvements for the ACDC and BDD100k datasets.

Vidhi Rathore, Naresh Manwani

Principal Component Analysis (PCA) is a widely used method for dimensionality reduction, but it often overlooks fairness, especially when working with data that includes demographic characteristics. This can lead to biased representations that disproportionately affect certain groups. To address this issue, our approach incorporates Joint Eigenvalue Decomposition (JEVD), a technique that enables the simultaneous diagonalization of multiple matrices, ensuring fair and efficient representations. We formally show that the optimal solution of JEVD leads to a fair PCA solution. By integrating JEVD with PCA, we strike an optimal balance between preserving data structure and promoting fairness across diverse groups. We demonstrate that our method outperforms existing baseline approaches in fairness and representational quality on various datasets. It retains the core advantages of PCA while ensuring that sensitive demographic attributes do not create disparities in the reduced representation.

Abhijit Manatkar, Devarsh Patel, Hima Patel et al.

Automating end-to-end Exploratory Data Analysis (AutoEDA) is a challenging open problem, often tackled through Reinforcement Learning (RL) by learning to predict a sequence of analysis operations (FILTER, GROUP, etc). Defining rewards for each operation is a challenging task and existing methods rely on various \emph{interestingness measures} to craft reward functions to capture the importance of each operation. In this work, we argue that not all of the essential features of what makes an operation important can be accurately captured mathematically using rewards. We propose an AutoEDA model trained through imitation learning from expert EDA sessions, bypassing the need for manually defined interestingness measures. Our method, based on generative adversarial imitation learning (GAIL), generalizes well across datasets, even with limited expert data. We also introduce a novel approach for generating synthetic EDA demonstrations for training. Our method outperforms the existing state-of-the-art end-to-end EDA approach on benchmarks by upto 3x, showing strong performance and generalization, while naturally capturing diverse interestingness measures in generated EDA sessions.

Vrund Shah, Tejas Chaudhari, Naresh Manwani

Robustness towards adversarial attacks is a vital property for classifiers in several applications such as autonomous driving, medical diagnosis, etc. Also, in such scenarios, where the cost of misclassification is very high, knowing when to abstain from prediction becomes crucial. A natural question is which surrogates can be used to ensure learning in scenarios where the input points are adversarially perturbed and the classifier can abstain from prediction? This paper aims to characterize and design surrogates calibrated in "Adversarial Robust Reject Option" setting. First, we propose an adversarial robust reject option loss $\ell_{d}^γ$ and analyze it for the hypothesis set of linear classifiers ($\mathcal{H}_{\textrm{lin}}$). Next, we provide a complete characterization result for any surrogate to be $(\ell_{d}^γ,\mathcal{H}_{\textrm{lin}})$- calibrated. To demonstrate the difficulty in designing surrogates to $\ell_{d}^γ$, we show negative calibration results for convex surrogates and quasi-concave conditional risk cases (these gave positive calibration in adversarial setting without reject option). We also empirically argue that Shifted Double Ramp Loss (DRL) and Shifted Double Sigmoid Loss (DSL) satisfy the calibration conditions. Finally, we demonstrate the robustness of shifted DRL and shifted DSL against adversarial perturbations on a synthetically generated dataset.

Uday Bhaskar, Varul Srivastava, Avyukta Manjunatha Vummintala et al.

Federated Learning (FL) emerged as a learning method to enable the server to train models over data distributed among various clients. These clients are protective about their data being leaked to the server, any other client, or an external adversary, and hence, locally train the model and share it with the server rather than sharing the data. The introduction of sophisticated inferencing attacks enabled the leakage of information about data through access to model parameters. To tackle this challenge, privacy-preserving federated learning aims to achieve differential privacy through learning algorithms like DP-SGD. However, such methods involve adding noise to the model, data, or gradients, reducing the model's performance. This work provides a theoretical analysis of the tradeoff between model performance and communication complexity of the FL system. We formally prove that training for one local epoch per global round of training gives optimal performance while preserving the same privacy budget. We also investigate the change of utility (tied to privacy) of FL models with a change in the number of clients and observe that when clients are training using DP-SGD and argue that for the same privacy budget, the utility improved with increased clients. We validate our findings through experiments on real-world datasets. The results from this paper aim to improve the performance of privacy-preserving federated learning systems.

Jayadratha Gayen, Himanshu Pal, Naresh Manwani et al.

Many real-world systems can be modeled as dynamic graphs, where nodes and edges evolve over time, requiring specialized models to capture their evolving dynamics in risk-sensitive applications effectively. Temporal graph neural networks (GNNs) are one such category of specialized models. For the first time, our approach integrates a reject option strategy within the framework of GNNs for continuous-time dynamic graphs. This allows the model to strategically abstain from making predictions when the uncertainty is high and confidence is low, thus minimizing the risk of critical misclassification and enhancing the results and reliability. We propose a coverage-based abstention prediction model to implement the reject option that maximizes prediction within a specified coverage. It improves the prediction score for link prediction and node classification tasks. Temporal GNNs deal with extremely skewed datasets for the next state prediction or node classification task. In the case of class imbalance, our method can be further tuned to provide a higher weightage to the minority class. Exhaustive experiments are presented on four datasets for dynamic link prediction and two datasets for dynamic node classification tasks. This demonstrates the effectiveness of our approach in improving the reliability and area under the curve (AUC)/ average precision (AP) scores for predictions in dynamic graph scenarios. The results highlight our model's ability to efficiently handle the trade-offs between prediction confidence and coverage, making it a dependable solution for applications requiring high precision in dynamic and uncertain environments.

Uday Bhaskar, Jayadratha Gayen, Charu Sharma et al.

One of the key tasks in graph learning is node classification. While Graph neural networks have been used for various applications, their adaptivity to reject option setting is not previously explored. In this paper, we propose NCwR, a novel approach to node classification in Graph Neural Networks (GNNs) with an integrated reject option, which allows the model to abstain from making predictions when uncertainty is high. We propose both cost-based and coverage-based methods for classification with abstention in node classification setting using GNNs. We perform experiments using our method on three standard citation network datasets Cora, Citeseer and Pubmed and compare with relevant baselines. We also model the Legal judgment prediction problem on ILDC dataset as a node classification problem where nodes represent legal cases and edges represent citations. We further interpret the model by analyzing the cases that the model abstains from predicting by visualizing which part of the input features influenced this decision.

Darshana Saravanan, Naresh Manwani, Vineet Gandhi

We motivate weakly supervised learning as an effective learning paradigm for problems where curating perfectly annotated datasets is expensive and may require domain expertise such as fine-grained classification. We focus on Partial Label Learning (PLL), a weakly-supervised learning paradigm where each training instance is paired with a set of candidate labels (partial label), one of which is the true label. Noisy PLL (NPLL) relaxes this constraint by allowing some partial labels to not contain the true label, enhancing the practicality of the problem. Our work centres on NPLL and presents a framework that initially assigns pseudo-labels to images by exploiting the noisy partial labels through a weighted nearest neighbour algorithm. These pseudo-label and image pairs are then used to train a deep neural network classifier with label smoothing. The classifier's features and predictions are subsequently employed to refine and enhance the accuracy of pseudo-labels. We perform thorough experiments on seven datasets and compare against nine NPLL and PLL methods. We achieve state-of-the-art results in all studied settings from the prior literature, obtaining substantial gains in the simulated fine-grained benchmarks. Further, we show the promising generalisation capability of our framework in realistic, fine-grained, crowd-sourced datasets.

Bhavya Kalra, Kulin Shah, Naresh Manwani

In this paper, we propose deep architectures for learning instance specific abstain (reject option) binary classifiers. The proposed approach uses double sigmoid loss function as described by Kulin Shah and Naresh Manwani in ("Online Active Learning of Reject Option Classifiers", AAAI, 2020), as a performance measure. We show that the double sigmoid loss is classification calibrated. We also show that the excess risk of 0-d-1 loss is upper bounded by the excess risk of double sigmoid loss. We derive the generalization error bounds for the proposed architecture for reject option classifiers. To show the effectiveness of the proposed approach, we experiment with several real world datasets. We observe that the proposed approach not only performs comparable to the state-of-the-art approaches, it is also robust against label noise. We also provide visualizations to observe the important features learned by the network corresponding to the abstaining decision.

Gaurav Batra, Naresh Manwani

This paper introduces a new online learning framework for multiclass classification called learning with diluted bandit feedback. At every time step, the algorithm predicts a candidate label set instead of a single label for the observed example. It then receives feedback from the environment whether the actual label lies in this candidate label set or not. This feedback is called "diluted bandit feedback". Learning in this setting is even more challenging than the bandit feedback setting, as there is more uncertainty in the supervision. We propose an algorithm for multiclass classification using dilute bandit feedback (MC-DBF), which uses the exploration-exploitation strategy to predict the candidate set in each trial. We show that the proposed algorithm achieves O(T^{1-\frac{1}{m+2}}) mistake bound if candidate label set size (in each step) is m. We demonstrate the effectiveness of the proposed approach with extensive simulations.

Sarath Sivaprasad, Ankur Singh, Naresh Manwani et al.

In this paper, we investigate a constrained formulation of neural networks where the output is a convex function of the input. We show that the convexity constraints can be enforced on both fully connected and convolutional layers, making them applicable to most architectures. The convexity constraints include restricting the weights (for all but the first layer) to be non-negative and using a non-decreasing convex activation function. Albeit simple, these constraints have profound implications on the generalization abilities of the network. We draw three valuable insights: (a) Input Output Convex Neural Networks (IOC-NNs) self regularize and reduce the problem of overfitting; (b) Although heavily constrained, they outperform the base multi layer perceptrons and achieve similar performance as compared to base convolutional architectures and (c) IOC-NNs show robustness to noise in train labels. We demonstrate the efficacy of the proposed idea using thorough experiments and ablation studies on standard image classification datasets with three different neural network architectures.

Mudit Agarwal, Naresh Manwani

This paper addresses the problem of multiclass classification with corrupted or noisy bandit feedback. In this setting, the learner may not receive true feedback. Instead, it receives feedback that has been flipped with some non-zero probability. We propose a novel approach to deal with noisy bandit feedback based on the unbiased estimator technique. We further offer a method that can efficiently estimate the noise rates, thus providing an end-to-end framework. The proposed algorithm enjoys a mistake bound of the order of $O(\sqrt{T})$ in the high noise case and of the order of $O(T^{\nicefrac{2}{3}})$ in the worst case. We show our approach's effectiveness using extensive experiments on several benchmark datasets.

Rajarshi Bhattacharjee, Naresh Manwani

In this paper, we propose online algorithms for multiclass classification using partial labels. We propose two variants of Perceptron called Avg Perceptron and Max Perceptron to deal with the partial labeled data. We also propose Avg Pegasos and Max Pegasos, which are extensions of Pegasos algorithm. We also provide mistake bounds for Avg Perceptron and regret bound for Avg Pegasos. We show the effectiveness of the proposed approaches by experimenting on various datasets and comparing them with the standard Perceptron and Pegasos.

Bhanu Garg, Naresh Manwani

The real-world data is often susceptible to label noise, which might constrict the effectiveness of the existing state of the art algorithms for ordinal regression. Existing works on ordinal regression do not take label noise into account. We propose a theoretically grounded approach for class conditional label noise in ordinal regression problems. We present a deep learning implementation of two commonly used loss functions for ordinal regression that is both - 1) robust to label noise, and 2) rank consistent for a good ranking rule. We verify these properties of the algorithm empirically and show robustness to label noise on real data and rank consistency. To the best of our knowledge, this is the first approach for robust ordinal regression models.

Subba Reddy Oota, Naresh Manwani, Raju S. Bapi

fMRI semantic category understanding using linguistic encoding models attempts to learn a forward mapping that relates stimuli to the corresponding brain activation. State-of-the-art encoding models use a single global model (linear or non-linear) to predict brain activation given the stimulus. However, the critical assumption in these methods is that a priori different brain regions respond the same way to all the stimuli, that is, there is no modularity or specialization assumed for any region. This goes against the modularity theory, supported by many cognitive neuroscience investigations suggesting that there are functionally specialized regions in the brain. In this paper, we achieve this by clustering similar regions together and for every cluster we learn a different linear regression model using a mixture of linear experts model. The key idea here is that each linear expert captures the behaviour of similar brain regions. Given a new stimulus, the utility of the proposed model is twofold (i) predicts the brain activation as a weighted linear combination of the activations of multiple linear experts and (ii) to learn multiple experts corresponding to different brain regions. We argue that each expert captures activity patterns related to a particular region of interest (ROI) in the human brain. This study helps in understanding the brain regions that are activated together given different kinds of stimuli. Importantly, we suggest that the mixture of regression experts (MoRE) framework successfully combines the two principles of organization of function in the brain, namely that of specialization and integration. Experiments on fMRI data from paradigm 1 [1]where participants view linguistic stimuli show that the proposed MoRE model has better prediction accuracy compared to that of conventional models.

Kulin Shah, Naresh Manwani

Active learning is an important technique to reduce the number of labeled examples in supervised learning. Active learning for binary classification has been well addressed in machine learning. However, active learning of the reject option classifier remains unaddressed. In this paper, we propose novel algorithms for active learning of reject option classifiers. We develop an active learning algorithm using double ramp loss function. We provide mistake bounds for this algorithm. We also propose a new loss function called double sigmoid loss function for reject option and corresponding active learning algorithm. We offer a convergence guarantee for this algorithm. We provide extensive experimental results to show the effectiveness of the proposed algorithms. The proposed algorithms efficiently reduce the number of label examples required.

Kulin Shah, P. S. Sastry, Naresh Manwani

In this paper, we propose a novel mixture of expert architecture for learning polyhedral classifiers. We learn the parameters of the classifierusing an expectation maximization algorithm. Wederive the generalization bounds of the proposedapproach. Through an extensive simulation study, we show that the proposed method performs comparably to other state-of-the-art approaches.

Subba Reddy Oota, Adithya Avvaru, Naresh Manwani et al.

fMRI semantic category understanding using linguistic encoding models attempt to learn a forward mapping that relates stimuli to the corresponding brain activation. Classical encoding models use linear multi-variate methods to predict the brain activation (all voxels) given the stimulus. However, these methods essentially assume multiple regions as one large uniform region or several independent regions, ignoring connections among them. In this paper, we present a mixture of experts-based model where a group of experts captures brain activity patterns related to particular regions of interest (ROI) and also show the discrimination across different experts. The model is trained word stimuli encoded as 25-dimensional feature vectors as input and the corresponding brain responses as output. Given a new word (25-dimensional feature vector), it predicts the entire brain activation as the linear combination of multiple experts brain activations. We argue that each expert learns a certain region of brain activations corresponding to its category of words, which solves the problem of identifying the regions with a simple encoding model. We showcase that proposed mixture of experts-based model indeed learns region-based experts to predict the brain activations with high spatial accuracy.

Naresh Manwani, Mohit Chandra

In this paper, we propose exact passive-aggressive (PA) online algorithms for learning to rank. The proposed algorithms can be used even when we have interval labels instead of actual labels for examples. The proposed algorithms solve a convex optimization problem at every trial. We find exact solution to those optimization problems to determine the updated parameters. We propose support class algorithm (SCA) which finds the active constraints using the KKT conditions of the optimization problems. These active constrains form support set which determines the set of thresholds that need to be updated. We derive update rules for PA, PA-I and PA-II. We show that the proposed algorithms maintain the ordering of the thresholds after every trial. We provide the mistake bounds of the proposed algorithms in both ideal and general settings. We also show experimentally that the proposed algorithms successfully learn accurate classifiers using interval labels as well as exact labels. Proposed algorithms also do well compared to other approaches.

Subba Reddy Oota, Naresh Manwani, Bapi Raju S

The dispute of how the human brain represents conceptual knowledge has been argued in many scientific fields. Brain imaging studies have shown that the spatial patterns of neural activation in the brain are correlated with thinking about different semantic categories of words (for example, tools, animals, and buildings) or when viewing the related pictures. In this paper, we present a computational model that learns to predict the neural activation captured in functional magnetic resonance imaging (fMRI) data of test words. Unlike the models with hand-crafted features that have been used in the literature, in this paper we propose a novel approach wherein decoding models are built with features extracted from popular linguistic encodings of Word2Vec, GloVe, Meta-Embeddings in conjunction with the empirical fMRI data associated with viewing several dozen concrete nouns. We compared these models with several other models that use word features extracted from FastText, Randomly-generated features, Mitchell's 25 features [1]. The experimental results show that the predicted fMRI images using Meta-Embeddings meet the state-of-the-art performance. Although models with features from GloVe and Word2Vec predict fMRI images similar to the state-of-the-art model, model with features from Meta-Embeddings predicts significantly better. The proposed scheme that uses popular linguistic encoding offers a simple and easy approach for semantic decoding from fMRI experiments.

Kulin Shah, Naresh Manwani

In this paper, we propose an approach for learning sparse reject option classifiers using double ramp loss $L_{dr}$. We use DC programming to find the risk minimizer. The algorithm solves a sequence of linear programs to learn the reject option classifier. We show that the loss $L_{dr}$ is Fisher consistent. We also show that the excess risk of loss $L_d$ is upper bounded by the excess risk of $L_{dr}$. We derive the generalization error bounds for the proposed approach. We show the effectiveness of the proposed approach by experimenting it on several real world datasets. The proposed approach not only performs comparable to the state of the art but it also successfully learns sparse classifiers.

Naresh Manwani

In this paper, we propose an online learning algorithm PRIL for learning ranking classifiers using interval labeled data and show its correctness. We show its convergence in finite number of steps if there exists an ideal classifier such that the rank given by it for an example always lies in its label interval. We then generalize this mistake bound result for the general case. We also provide regret bound for the proposed algorithm. We propose a multiplicative update algorithm for PRIL called M-PRIL. We provide its correctness and convergence results. We show the effectiveness of PRIL by showing its performance on various datasets.

Aritra Ghosh, Naresh Manwani, P. S. Sastry

In most practical problems of classifier learning, the training data suffers from the label noise. Hence, it is important to understand how robust is a learning algorithm to such label noise. This paper presents some theoretical analysis to show that many popular decision tree algorithms are robust to symmetric label noise under large sample size. We also present some sample complexity results which provide some bounds on the sample size for the robustness to hold with a high probability. Through extensive simulations we illustrate this robustness.

Aritra Ghosh, Naresh Manwani, P. S. Sastry

In many applications, the training data, from which one needs to learn a classifier, is corrupted with label noise. Many standard algorithms such as SVM perform poorly in presence of label noise. In this paper we investigate the robustness of risk minimization to label noise. We prove a sufficient condition on a loss function for the risk minimization under that loss to be tolerant to uniform label noise. We show that the $0-1$ loss, sigmoid loss, ramp loss and probit loss satisfy this condition though none of the standard convex loss functions satisfy it. We also prove that, by choosing a sufficiently large value of a parameter in the loss function, the sigmoid loss, ramp loss and probit loss can be made tolerant to non-uniform label noise also if we can assume the classes to be separable under noise-free data distribution. Through extensive empirical studies, we show that risk minimization under the $0-1$ loss, the sigmoid loss and the ramp loss has much better robustness to label noise when compared to the SVM algorithm.

Naresh Manwani, Kalpit Desai, Sanand Sasidharan et al.

We consider the problem of learning reject option classifiers. The goodness of a reject option classifier is quantified using $0-d-1$ loss function wherein a loss $d \in (0,.5)$ is assigned for rejection. In this paper, we propose {\em double ramp loss} function which gives a continuous upper bound for $(0-d-1)$ loss. Our approach is based on minimizing regularized risk under the double ramp loss using {\em difference of convex (DC) programming}. We show the effectiveness of our approach through experiments on synthetic and benchmark datasets. Our approach performs better than the state of the art reject option classification approaches.