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Convergence rate of stochastic k-meansworkpreprint / 2016 / arXiv PrismAgent: Illuminating Harm in Memes via a Zero-Shot Interpretable Multi-Agent Frameworkworkpreprint / 2026 / arXiv PACE: Prune-And-Compress Ensemble Modelsworkpreprint / 2026 / arXiv Machine Learningtopic49008 works

preprint2016arXiv

Convergence rate of stochastic k-means

We analyze online \cite{BottouBengio} and mini-batch \cite{Sculley} $k$-means variants. Both scale up the widely used $k$-means algorithm via stochastic approximation, and have become popular for large-scale clustering and unsupervised feature learning. We show, for the first time, that starting with any initial solution, they converge to a "local optimum" at rate $O(\frac{1}{t})$ (in terms of the $k$-means objective) under general conditions. In addition, we show if the dataset is clusterable, when initialized with a simple and scalable seeding algorithm, mini-batch $k$-means converges to an optimal $k$-means solution at rate $O(\frac{1}{t})$ with high probability. The $k$-means objective is non-convex and non-differentiable: we exploit ideas from recent work on stochastic gradient descent for non-convex problems \cite{ge:sgd_tensor, balsubramani13} by providing a novel characterization of the trajectory of $k$-means algorithm on its solution space, and circumvent the non-differentiability problem via geometric insights about $k$-means update.

preprint2026arXiv

PrismAgent: Illuminating Harm in Memes via a Zero-Shot Interpretable Multi-Agent Framework

The rapid spread of memes makes harmful content detection increasingly crucial, as effective identification can curb the circulation of misinformation. However, existing methods rely heavily on high-volume annotated data, which leads to substantial training costs and limited generalization. To address these challenges, we propose PrismAgent, a zero-shot, multi-agent, interpretable framework. PrismAgent conceptualizes this task as a criminal case investigation, employing four specialized agents responsible for the analysis, investigation, prosecution, and judgment stages within a structured collaborative workflow. In the first stage, the analyst agent paraphrases each meme under benevolent and malicious assumptions to probe its underlying intent. The investigator agent then retrieves supporting evidence from an unannotated dataset and constructs contextual interpretations for the meme and its variants. Next, the prosecutor agent performs three independent preliminary judgments by pairing the original meme with each of the three interpretations. Finally, the judge agent deliberates across all evidence to render a final verdict. Moreover, PrismAgent's explicit multi-stage reasoning chain makes the model inherently interpretable, as every intermediate step is explicitly explained rather than only producing a final detection result. Extensive experiments on three public datasets show that PrismAgent significantly outperforms existing zero-shot detection methods.

preprint2026arXiv

PACE: Prune-And-Compress Ensemble Models

Ensemble models achieve state-of-the-art performance on prediction tasks, but usually require aggregating a large number of weak learners. This can hinder deployment, interpretability, and downstream tasks such as robustness verification. Remedies to this issue fall into two main camps: pruning, which discards redundant learners, and compression, which generates new ones from scratch. We introduce PACE, a framework that interleaves these paradigms in a two-phase strategy. First, new learners are actively generated via a theoretically grounded procedure to enhance the diversity of the initial ensemble. When no more relevant learners can be found, a second phase of pruning is performed on this enriched ensemble. During both operations, PACE allows fine control on the faithfulness to the original ensemble. Experiments show that our method outperforms prior pruning and compression methods while offering principled control of faithfulness guarantees.

preprint2022arXiv

Modeling Irregular Time Series with Continuous Recurrent Units

Recurrent neural networks (RNNs) are a popular choice for modeling sequential data. Modern RNN architectures assume constant time-intervals between observations. However, in many datasets (e.g. medical records) observation times are irregular and can carry important information. To address this challenge, we propose continuous recurrent units (CRUs) -- a neural architecture that can naturally handle irregular intervals between observations. The CRU assumes a hidden state, which evolves according to a linear stochastic differential equation and is integrated into an encoder-decoder framework. The recursive computations of the CRU can be derived using the continuous-discrete Kalman filter and are in closed form. The resulting recurrent architecture has temporal continuity between hidden states and a gating mechanism that can optimally integrate noisy observations. We derive an efficient parameterization scheme for the CRU that leads to a fast implementation f-CRU. We empirically study the CRU on a number of challenging datasets and find that it can interpolate irregular time series better than methods based on neural ordinary differential equations.

preprint2022arXiv

Embedded Ensembles: Infinite Width Limit and Operating Regimes

A memory efficient approach to ensembling neural networks is to share most weights among the ensembled models by means of a single reference network. We refer to this strategy as Embedded Ensembling (EE); its particular examples are BatchEnsembles and Monte-Carlo dropout ensembles. In this paper we perform a systematic theoretical and empirical analysis of embedded ensembles with different number of models. Theoretically, we use a Neural-Tangent-Kernel-based approach to derive the wide network limit of the gradient descent dynamics. In this limit, we identify two ensemble regimes - independent and collective - depending on the architecture and initialization strategy of ensemble models. We prove that in the independent regime the embedded ensemble behaves as an ensemble of independent models. We confirm our theoretical prediction with a wide range of experiments with finite networks, and further study empirically various effects such as transition between the two regimes, scaling of ensemble performance with the network width and number of models, and dependence of performance on a number of architecture and hyperparameter choices.

preprint2013arXiv

Convex vs nonconvex approaches for sparse estimation: GLasso, Multiple Kernel Learning and Hyperparameter GLasso

The popular Lasso approach for sparse estimation can be derived via marginalization of a joint density associated with a particular stochastic model. A different marginalization of the same probabilistic model leads to a different non-convex estimator where hyperparameters are optimized. Extending these arguments to problems where groups of variables have to be estimated, we study a computational scheme for sparse estimation that differs from the Group Lasso. Although the underlying optimization problem defining this estimator is non-convex, an initialization strategy based on a univariate Bayesian forward selection scheme is presented. This also allows us to define an effective non-convex estimator where only one scalar variable is involved in the optimization process. Theoretical arguments, independent of the correctness of the priors entering the sparse model, are included to clarify the advantages of this non-convex technique in comparison with other convex estimators. Numerical experiments are also used to compare the performance of these approaches.

preprint2020arXiv

Bandit Samplers for Training Graph Neural Networks

Several sampling algorithms with variance reduction have been proposed for accelerating the training of Graph Convolution Networks (GCNs). However, due to the intractable computation of optimal sampling distribution, these sampling algorithms are suboptimal for GCNs and are not applicable to more general graph neural networks (GNNs) where the message aggregator contains learned weights rather than fixed weights, such as Graph Attention Networks (GAT). The fundamental reason is that the embeddings of the neighbors or learned weights involved in the optimal sampling distribution are changing during the training and not known a priori, but only partially observed when sampled, thus making the derivation of an optimal variance reduced samplers non-trivial. In this paper, we formulate the optimization of the sampling variance as an adversary bandit problem, where the rewards are related to the node embeddings and learned weights, and can vary constantly. Thus a good sampler needs to acquire variance information about more neighbors (exploration) while at the same time optimizing the immediate sampling variance (exploit). We theoretically show that our algorithm asymptotically approaches

preprint2020arXiv

Multi-Label Sampling based on Local Label Imbalance

Class imbalance is an inherent characteristic of multi-label data that hinders most multi-label learning methods. One efficient and flexible strategy to deal with this problem is to employ sampling techniques before training a multi-label learning model. Although existing multi-label sampling approaches alleviate the global imbalance of multi-label datasets, it is actually the imbalance level within the local neighbourhood of minority class examples that plays a key role in performance degradation. To address this issue, we propose a novel measure to assess the local label imbalance of multi-label datasets, as well as two multi-label sampling approaches based on the local label imbalance, namely MLSOL and MLUL. By considering all informative labels, MLSOL creates more diverse and better labeled synthetic instances for difficult examples, while MLUL eliminates instances that are harmful to their local region. Experimental results on 13 multi-label datasets demonstrate the effectiveness of the proposed measure and sampling approaches for a variety of evaluation metrics, particularly in the case of an ensemble of classifiers trained on repeated samples of the original data.

preprint2022arXiv

StableMoE: Stable Routing Strategy for Mixture of Experts

The Mixture-of-Experts (MoE) technique can scale up the model size of Transformers with an affordable computational overhead. We point out that existing learning-to-route MoE methods suffer from the routing fluctuation issue, i.e., the target expert of the same input may change along with training, but only one expert will be activated for the input during inference. The routing fluctuation tends to harm sample efficiency because the same input updates different experts but only one is finally used. In this paper, we propose StableMoE with two training stages to address the routing fluctuation problem. In the first training stage, we learn a balanced and cohesive routing strategy and distill it into a lightweight router decoupled from the backbone model. In the second training stage, we utilize the distilled router to determine the token-to-expert assignment and freeze it for a stable routing strategy. We validate our method on language modeling and multilingual machine translation. The results show that StableMoE outperforms existing MoE methods in terms of both convergence speed and performance.

preprint2022arXiv

Alternating Mahalanobis Distance Minimization for Stable and Accurate CP Decomposition

CP decomposition (CPD) is prevalent in chemometrics, signal processing, data mining and many more fields. While many algorithms have been proposed to compute the CPD, alternating least squares (ALS) remains one of the most widely used algorithm for computing the decomposition. Recent works have introduced the notion of eigenvalues and singular values of a tensor and explored applications of eigenvectors and singular vectors in areas like signal processing, data analytics and in various other fields. We introduce a new formulation for deriving singular values and vectors of a tensor by considering the critical points of a function different from what is used in the previous work. Computing these critical points in an alternating manner motivates an alternating optimization algorithm which corresponds to alternating least squares algorithm in the matrix case. However, for tensors with order greater than equal to $3$, it minimizes an objective function which is different from the commonly used least squares loss. Alternating optimization of this new objective leads to simple updates to the factor matrices with the same asymptotic computational cost as ALS. We show that a subsweep of this algorithm can achieve a superlinear convergence rate for exact CPD with known rank and verify it experimentally. We then view the algorithm as optimizing a Mahalanobis distance with respect to each factor with ground metric dependent on the other factors. This perspective allows us to generalize our approach to interpolate between updates corresponding to the ALS and the new algorithm to manage the tradeoff between stability and fitness of the decomposition. Our experimental results show that for approximating synthetic and real-world tensors, this algorithm and its variants converge to a better conditioned decomposition with comparable and sometimes better fitness as compared to the ALS algorithm.

preprint2026arXiv

A new type of federated clustering: A non-model-sharing approach

In recent years, the growing need to leverage sensitive data across institutions has led to increased attention on federated learning (FL), a decentralized machine learning paradigm that enables model training without sharing raw data. However, existing FL-based clustering methods, known as federated clustering, typically assume simple data partitioning scenarios such as horizontal or vertical splits, and cannot handle more complex distributed structures. This study proposes data collaboration clustering (DC-Clustering), a novel federated clustering method that supports clustering over complex data partitioning scenarios where horizontal and vertical splits coexist. In DC-Clustering, each institution shares only intermediate representations instead of raw data, ensuring privacy preservation while enabling collaborative clustering. The method allows flexible selection between k-means and spectral clustering, and achieves final results with a single round of communication with the central server. We conducted extensive experiments using synthetic and open benchmark datasets. The results show that our method achieves clustering performance comparable to centralized clustering where al

preprint2022arXiv

Mitigating shortage of labeled data using clustering-based active learning with diversity exploration

In this paper, we proposed a new clustering-based active learning framework, namely Active Learning using a Clustering-based Sampling (ALCS), to address the shortage of labeled data. ALCS employs a density-based clustering approach to explore the cluster structure from the data without requiring exhaustive parameter tuning. A bi-cluster boundary-based sample query procedure is introduced to improve the learning performance for classifying highly overlapped classes. Additionally, we developed an effective diversity exploration strategy to address the redundancy among queried samples. Our experimental results justified the efficacy of the ALCS approach.

preprint2016arXiv

Multi-view Kernel Completion

In this paper, we introduce the first method that (1) can complete kernel matrices with completely missing rows and columns as opposed to individual missing kernel values, (2) does not require any of the kernels to be complete a priori, and (3) can tackle non-linear kernels. These aspects are necessary in practical applications such as integrating legacy data sets, learning under sensor failures and learning when measurements are costly for some of the views. The proposed approach predicts missing rows by modelling both within-view and between-view relationships among kernel values. We show, both on simulated data and real world data, that the proposed method outperforms existing techniques in the restricted settings where they are available, and extends applicability to new settings.

preprint2020arXiv

A Triangular Network For Density Estimation

We report a triangular neural network implementation of neural autoregressive flow (NAF). Unlike many universal autoregressive density models, our design is highly modular, parameter economy, computationally efficient, and applicable to density estimation of data with high dimensions. It achieves state-of-the-art bits-per-dimension indices on MNIST and CIFAR-10 (about 1.1 and 3.7, respectively) in the category of general-purpose density estimators.

preprint2020arXiv

Adaptive Bayesian Reticulum

Neural Networks and Decision Trees: two popular techniques for supervised learning that are seemingly disconnected in their formulation and optimization method, have recently been combined in a single construct. The connection pivots on assembling an artificial Neural Network with nodes that allow for a gate-like function to mimic a tree split, optimized using the standard approach of recursively applying the chain rule to update its parameters. Yet two main challenges have impeded wide use of this hybrid approach: (a) the inability of global gradient ascent techniques to optimize hierarchical parameters (as introduced by the gate function); and (b) the construction of the tree structure, which has relied on standard decision tree algorithms to learn the network topology or incrementally (and heuristically) searching the space at random. Here we propose a probabilistic construct that exploits the idea of a node's unexplained potential (the total error channeled through the node) in order to decide where to expand further, mimicking the standard tree construction in a Neural Network setting, alongside a modified gradient ascent that first locally optimizes an expanded node befor

preprint2022arXiv

Improving Correlation Capture in Generating Imbalanced Data using Differentially Private Conditional GANs

Despite the remarkable success of Generative Adversarial Networks (GANs) on text, images, and videos, generating high-quality tabular data is still under development owing to some unique challenges such as capturing dependencies in imbalanced data, optimizing the quality of synthetic patient data while preserving privacy. In this paper, we propose DP-CGANS, a differentially private conditional GAN framework consisting of data transformation, sampling, conditioning, and networks training to generate realistic and privacy-preserving tabular data. DP-CGANS distinguishes categorical and continuous variables and transforms them to latent space separately. Then, we structure a conditional vector as an additional input to not only presents the minority class in the imbalanced data, but also capture the dependency between variables. We inject statistical noise to the gradients in the networking training process of DP-CGANS to provide a differential privacy guarantee. We extensively evaluate our model with state-of-the-art generative models on three public datasets and two real-world personal health datasets in terms of statistical similarity, machine learning performance, and privacy measurement. We demonstrate that our model outperforms other comparable models, especially in capturing dependency between variables. Finally, we present the balance between data utility and privacy in synthetic data generation considering the different data structure and characteristics of real-world datasets such as imbalance variables, abnormal distributions, and sparsity of data.

preprint2014arXiv

Median Selection Subset Aggregation for Parallel Inference

For massive data sets, efficient computation commonly relies on distributed algorithms that store and process subsets of the data on different machines, minimizing communication costs. Our focus is on regression and classification problems involving many features. A variety of distributed algorithms have been proposed in this context, but challenges arise in defining an algorithm with low communication, theoretical guarantees and excellent practical performance in general settings. We propose a MEdian Selection Subset AGgregation Estimator (message) algorithm, which attempts to solve these problems. The algorithm applies feature selection in parallel for each subset using Lasso or another method, calculates the `median' feature inclusion index, estimates coefficients for the selected features in parallel for each subset, and then averages these estimates. The algorithm is simple, involves very minimal communication, scales efficiently in both sample and feature size, and has theoretical guarantees. In particular, we show model selection consistency and coefficient estimation efficiency. Extensive experiments show excellent performance in variable selection, estimation, predicti

preprint2022arXiv

Actor-Critic based Improper Reinforcement Learning

We consider an improper reinforcement learning setting where a learner is given $M$ base controllers for an unknown Markov decision process, and wishes to combine them optimally to produce a potentially new controller that can outperform each of the base ones. This can be useful in tuning across controllers, learnt possibly in mismatched or simulated environments, to obtain a good controller for a given target environment with relatively few trials. Towards this, we propose two algorithms: (1) a Policy Gradient-based approach; and (2) an algorithm that can switch between a simple Actor-Critic (AC) based scheme and a Natural Actor-Critic (NAC) scheme depending on the available information. Both algorithms operate over a class of improper mixtures of the given controllers. For the first case, we derive convergence rate guarantees assuming access to a gradient oracle. For the AC-based approach we provide convergence rate guarantees to a stationary point in the basic AC case and to a global optimum in the NAC case. Numerical results on (i) the standard control theoretic benchmark of stabilizing an cartpole; and (ii) a constrained queueing task show that our improper policy optimization algorithm can stabilize the system even when the base policies at its disposal are unstable.

preprint2022arXiv

Deep Normed Embeddings for Patient Representation

We introduce a novel contrastive representation learning objective and a training scheme for clinical time series. Specifically, we project high dimensional EHR. data to a closed unit ball of low dimension, encoding geometric priors so that the origin represents an idealized perfect health state and the Euclidean norm is associated with the patient's mortality risk. Moreover, using septic patients as an example, we show how we could learn to associate the angle between two vectors with the different organ system failures, thereby, learning a compact representation which is indicative of both mortality risk and specific organ failure. We show how the learned embedding can be used for online patient monitoring, can supplement clinicians and improve performance of downstream machine learning tasks. This work was partially motivated from the desire and the need to introduce a systematic way of defining intermediate rewards for Reinforcement Learning in critical care medicine. Hence, we also show how such a design in terms of the learned embedding can result in qualitatively different policies and value distributions, as compared with using only terminal rewards.

preprint2020arXiv

A Comparison of Metric Learning Loss Functions for End-To-End Speaker Verification

Despite the growing popularity of metric learning approaches, very little work has attempted to perform a fair comparison of these techniques for speaker verification. We try to fill this gap and compare several metric learning loss functions in a systematic manner on the VoxCeleb dataset. The first family of loss functions is derived from the cross entropy loss (usually used for supervised classification) and includes the congenerous cosine loss, the additive angular margin loss, and the center loss. The second family of loss functions focuses on the similarity between training samples and includes the contrastive loss and the triplet loss. We show that the additive angular margin loss function outperforms all other loss functions in the study, while learning more robust representations. Based on a combination of SincNet trainable features and the x-vector architecture, the network used in this paper brings us a step closer to a really-end-to-end speaker verification system, when combined with the additive angular margin loss, while still being competitive with the x-vector baseline. In the spirit of reproducible research, we also release open source Python code for reproducing ou

preprint2020arXiv

Leveraging Multi-Source Weak Social Supervision for Early Detection of Fake News

Social media has greatly enabled people to participate in online activities at an unprecedented rate. However, this unrestricted access also exacerbates the spread of misinformation and fake news online which might cause confusion and chaos unless being detected early for its mitigation. Given the rapidly evolving nature of news events and the limited amount of annotated data, state-of-the-art systems on fake news detection face challenges due to the lack of large numbers of annotated training instances that are hard to come by for early detection. In this work, we exploit multiple weak signals from different sources given by user and content engagements (referred to as weak social supervision), and their complementary utilities to detect fake news. We jointly leverage the limited amount of clean data along with weak signals from social engagements to train deep neural networks in a meta-learning framework to estimate the quality of different weak instances. Experiments on realworld datasets demonstrate that the proposed framework outperforms state-of-the-art baselines for early detection of fake news without using any user engagements at prediction time.

preprint2020arXiv

Privacy Preserving K-Means Clustering: A Secure Multi-Party Computation Approach

Knowledge discovery is one of the main goals of Artificial Intelligence. This Knowledge is usually stored in databases spread in different environments, being a tedious (or impossible) task to access and extract data from them. To this difficulty we must add that these datasources may contain private data, therefore the information can never leave the source. Privacy Preserving Machine Learning (PPML) helps to overcome this difficulty, employing cryptographic techniques, allowing knowledge discovery while ensuring data privacy. K-means is one of the data mining techniques used in order to discover knowledge, grouping data points in clusters that contain similar features. This paper focuses in Privacy Preserving Machine Learning applied to K-means using recent protocols from the field of criptography. The algorithm is applied to different scenarios where data may be distributed either horizontally or vertically.

preprint2022arXiv

Predicting extreme events from data using deep machine learning: when and where

We develop a deep convolutional neural network (DCNN) based framework for model-free prediction of the occurrence of extreme events both in time ("when") and in space ("where") in nonlinear physical systems of spatial dimension two. The measurements or data are a set of two-dimensional snapshots or images. For a desired time horizon of prediction, a proper labeling scheme can be designated to enable successful training of the DCNN and subsequent prediction of extreme events in time. Given that an extreme event has been predicted to occur within the time horizon, a space-based labeling scheme can be applied to predict, within certain resolution, the location at which the event will occur. We use synthetic data from the 2D complex Ginzburg-Landau equation and empirical wind speed data of the North Atlantic ocean to demonstrate and validate our machine-learning based prediction framework. The trade-offs among the prediction horizon, spatial resolution, and accuracy are illustrated, and the detrimental effect of spatially biased occurrence of extreme event on prediction accuracy is discussed. The deep learning framework is viable for predicting extreme events in the real world.

preprint2014arXiv

Generative Modelling for Unsupervised Score Calibration

Score calibration enables automatic speaker recognizers to make cost-effective accept / reject decisions. Traditional calibration requires supervised data, which is an expensive resource. We propose a 2-component GMM for unsupervised calibration and demonstrate good performance relative to a supervised baseline on NIST SRE'10 and SRE'12. A Bayesian analysis demonstrates that the uncertainty associated with the unsupervised calibration parameter estimates is surprisingly small.

preprint2022arXiv

Analytically Integratable Zero-restlength Springs for Capturing Dynamic Modes unrepresented by Quasistatic Neural Networks

We present a novel paradigm for modeling certain types of dynamic simulation in real-time with the aid of neural networks. In order to significantly reduce the requirements on data (especially time-dependent data), as well as decrease generalization error, our approach utilizes a data-driven neural network only to capture quasistatic information (instead of dynamic or time-dependent information). Subsequently, we augment our quasistatic neural network (QNN) inference with a (real-time) dynamic simulation layer. Our key insight is that the dynamic modes lost when using a QNN approximation can be captured with a quite simple (and decoupled) zero-restlength spring model, which can be integrated analytically (as opposed to numerically) and thus has no time-step stability restrictions. Additionally, we demonstrate that the spring constitutive parameters can be robustly learned from a surprisingly small amount of dynamic simulation data. Although we illustrate the efficacy of our approach by considering soft-tissue dynamics on animated human bodies, the paradigm is extensible to many different simulation frameworks.

preprint2023arXiv

Bayesian Active Learning with Fully Bayesian Gaussian Processes

The bias-variance trade-off is a well-known problem in machine learning that only gets more pronounced the less available data there is. In active learning, where labeled data is scarce or difficult to obtain, neglecting this trade-off can cause inefficient and non-optimal querying, leading to unnecessary data labeling. In this paper, we focus on active learning with Gaussian Processes (GPs). For the GP, the bias-variance trade-off is made by optimization of the two hyperparameters: the length scale and noise-term. Considering that the optimal mode of the joint posterior of the hyperparameters is equivalent to the optimal bias-variance trade-off, we approximate this joint posterior and utilize it to design two new acquisition functions. The first one is a Bayesian variant of Query-by-Committee (B-QBC), and the second is an extension that explicitly minimizes the predictive variance through a Query by Mixture of Gaussian Processes (QB-MGP) formulation. Across six simulators, we empirically show that B-QBC, on average, achieves the best marginal likelihood, whereas QB-MGP achieves the best predictive performance. We show that incorporating the bias-variance trade-off in the acquisition functions mitigates unnecessary and expensive data labeling.

preprint2022arXiv

Benchmarking learned non-Cartesian k-space trajectories and reconstruction networks

We benchmark the current existing methods to jointly learn non-Cartesian k-space trajectory and reconstruction: PILOT, BJORK, and compare them with those obtained from the recently developed generalized hybrid learning (HybLearn) framework. We present the advantages of using projected gradient descent to enforce MR scanner hardware constraints as compared to using added penalties in the cost function. Further, we use the novel HybLearn scheme to jointly learn and compare our results through a retrospective study on fastMRI validation dataset.

preprint2020arXiv

Learning with Differentiable Perturbed Optimizers

Machine learning pipelines often rely on optimization procedures to make discrete decisions (e.g., sorting, picking closest neighbors, or shortest paths). Although these discrete decisions are easily computed, they break the back-propagation of computational graphs. In order to expand the scope of learning problems that can be solved in an end-to-end fashion, we propose a systematic method to transform optimizers into operations that are differentiable and never locally constant. Our approach relies on stochastically perturbed optimizers, and can be used readily together with existing solvers. Their derivatives can be evaluated efficiently, and smoothness tuned via the chosen noise amplitude. We also show how this framework can be connected to a family of losses developed in structured prediction, and give theoretical guarantees for their use in learning tasks. We demonstrate experimentally the performance of our approach on various tasks.

preprint2012arXiv

Positivity and Transportation

We prove in this paper that the weighted volume of the set of integral transportation matrices between two integral histograms r and c of equal sum is a positive definite kernel of r and c when the set of considered weights forms a positive definite matrix. The computation of this quantity, despite being the subject of a significant research effort in algebraic statistics, remains an intractable challenge for histograms of even modest dimensions. We propose an alternative kernel which, rather than considering all matrices of the transportation polytope, only focuses on a sub-sample of its vertices known as its Northwestern corner solutions. The resulting kernel is positive definite and can be computed with a number of operations O(R^2d) that grows linearly in the complexity of the dimension d, where R^2, the total amount of sampled vertices, is a parameter that controls the complexity of the kernel.

preprint2020arXiv

A Topology Layer for Machine Learning

Topology applied to real world data using persistent homology has started to find applications within machine learning, including deep learning. We present a differentiable topology layer that computes persistent homology based on level set filtrations and edge-based filtrations. We present three novel applications: the topological layer can (i) regularize data reconstruction or the weights of machine learning models, (ii) construct a loss on the output of a deep generative network to incorporate topological priors, and (iii) perform topological adversarial attacks on deep networks trained with persistence features. The code (www.github.com/bruel-gabrielsson/TopologyLayer) is publicly available and we hope its availability will facilitate the use of persistent homology in deep learning and other gradient based applications.

preprint2012arXiv

Parameter-Free Spectral Kernel Learning

Due to the growing ubiquity of unlabeled data, learning with unlabeled data is attracting increasing attention in machine learning. In this paper, we propose a novel semi-supervised kernel learning method which can seamlessly combine manifold structure of unlabeled data and Regularized Least-Squares (RLS) to learn a new kernel. Interestingly, the new kernel matrix can be obtained analytically with the use of spectral decomposition of graph Laplacian matrix. Hence, the proposed algorithm does not require any numerical optimization solvers. Moreover, by maximizing kernel target alignment on labeled data, we can also learn model parameters automatically with a closed-form solution. For a given graph Laplacian matrix, our proposed method does not need to tune any model parameter including the tradeoff parameter in RLS and the balance parameter for unlabeled data. Extensive experiments on ten benchmark datasets show that our proposed two-stage parameter-free spectral kernel learning algorithm can obtain comparable performance with fine-tuned manifold regularization methods in transductive setting, and outperform multiple kernel learning in supervised setting.

preprint2022arXiv

Dynamic Batch Adaptation

Current deep learning adaptive optimizer methods adjust the step magnitude of parameter updates by altering the effective learning rate used by each parameter. Motivated by the known inverse relation between batch size and learning rate on update step magnitudes, we introduce a novel training procedure that dynamically decides the dimension and the composition of the current update step. Our procedure, Dynamic Batch Adaptation (DBA) analyzes the gradients of every sample and selects the subset that best improves certain metrics such as gradient variance for each layer of the network. We present results showing DBA significantly improves the speed of model convergence. Additionally, we find that DBA produces an increased improvement over standard optimizers when used in data scarce conditions where, in addition to convergence speed, it also significantly improves model generalization, managing to train a network with a single fully connected hidden layer using only 1% of the MNIST dataset to reach 97.79% test accuracy. In an even more extreme scenario, it manages to reach 97.44% test accuracy using only 10 samples per class. These results represent a relative error rate reduction of 81.78% and 88.07% respectively, compared to the standard optimizers, Stochastic Gradient Descent (SGD) and Adam.