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Researcher profile

Lorenzo Rosasco

Lorenzo Rosasco contributes to research discovery and scholarly infrastructure.

ResearcherAffiliation not importedOpen to collaborate
Machine Learningmath.OCComputer Visionmath.FAmath.STStatistics TheoryArtificial Intelligencemath.DSmath.NANumerical Analysisphysics.ao-phRobotics

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Published work

24 published item(s)

preprint2026arXiv

A New Formulation for Zeroth-Order Optimization of Adversarial EXEmples in Malware Detection

Machine learning malware detectors are vulnerable to adversarial EXEmples, i.e., carefully-crafted Windows programs tailored to evade detection. Unlike other adversarial problems, attacks in this context must be functionality-preserving, a constraint that is challenging to address. As a consequence, heuristic algorithms are typically used, which inject new content, either randomly-picked or harvested from legitimate programs. In this paper, we show how learning malware detectors can be cast within a zeroth-order optimization framework, which allows incorporating functionality-preserving manipulations. This permits the deployment of sound and efficient gradient-free optimization algorithms, which come with theoretical guarantees and allow for minimal hyper-parameters tuning. As a by-product, we propose and study ZEXE, a novel zeroth-order attack against Windows malware detection. Compared to state-of-the-art techniques, ZEXE provides improvement in the evasion rate, reducing to less than one third the size of the injected content.

0 citations0 reviewsNo code linkedOpen access
preprint2026arXiv

Dynamic robotic cloth folding with efficient Koopman operator-based model predictive control

Robotic cloth folding is a challenging task, particularly when considering dynamic folding tasks, which aim at folding cloth by fast motions that leverage its dynamics. When subject to such fast motions, the complexity of cloth dynamics hinders both system identification and planning of folding trajectories, resulting in a difficult simulation-to-reality transfer when using physical models of cloth. Compared to the dexterity that humans exhibit when performing folding tasks, robotic approaches usually employ small garments with quite rigid dynamics, and are either too slow, or fast but imprecise, requiring several attempts to achieve a reasonably good fold. In this paper, we tackle these challenges by generating fast folding trajectories with a novel model predictive controller, integrating physics-based simulation of cloth dynamics and efficient, kernel-based Koopman operator regression. Koopman operator regression, an increasingly popular machine learning technique for nonlinear system identification, is used to obtain a linear model for the cloth being folded. Such a surrogate model, trained with data from a high-fidelity, physics-based cloth simulator, can then be employed within a suitable model predictive control algorithm, in place of the costly, nonlinear one, to efficiently generate folding trajectories to be executed by a robotic manipulator. Both in simulated and real-robot experiments, we show how the linearization supplied by the Koopman operator-based model can be employed to efficiently generate fast folding trajectories to unseen poses, without sacrificing folding accuracy.

0 citations0 reviewsNo code linkedOpen access
preprint2026arXiv

SGD for Variational Inference: Tackling Unbounded Variance via Preconditioning and Dynamic Batching

Black-Box Variational Inference (BBVI) typically relies on Stochastic Gradient Descent (SGD) to optimize the Evidence Lower Bound (ELBO). However, the stochastic gradients in BBVI inherently exhibit unbounded variance, violating standard assumptions and instead satisfying the weaker Blum-Gladyshev (BG) condition, where variance grows quadratically with distance from the optimum. In this paper, we bridge the gap between stochastic optimization theory and the practical instances of BBVI. Focusing on the broad elliptic location-scale family of parameterized distributions, we offer two main contributions. First, we prove the existence of an ELBO solution, a foundational property usually assumed a priori in the literature. Second, we establish comprehensive convergence guarantees spanning finite-time and asymptotic regimes for Minibatch Projected SGD (PSGD) equipped with dynamic batching and preconditioning under the BG condition. Our theoretical framework demonstrates that dynamic batching combined with preconditioning systematically enables rigorous guarantees even in complex settings. We illustrate our theoretical findings with numerical results, highlighting the efficacy of our approach for modern inference tasks.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Ada-BKB: Scalable Gaussian Process Optimization on Continuous Domains by Adaptive Discretization

Gaussian process optimization is a successful class of algorithms(e.g. GP-UCB) to optimize a black-box function through sequential evaluations. However, for functions with continuous domains, Gaussian process optimization has to rely on either a fixed discretization of the space, or the solution of a non-convex optimization subproblem at each evaluation. The first approach can negatively affect performance, while the second approach requires a heavy computational burden. A third option, only recently theoretically studied, is to adaptively discretize the function domain. Even though this approach avoids the extra non-convex optimization costs, the overall computational complexity is still prohibitive. An algorithm such as GP-UCB has a runtime of $O(T^4)$, where $T$ is the number of iterations. In this paper, we introduce Ada-BKB (Adaptive Budgeted Kernelized Bandit), a no-regret Gaussian process optimization algorithm for functions on continuous domains, that provably runs in $O(T^2 d_\text{eff}^2)$, where $d_\text{eff}$ is the effective dimension of the explored space, and which is typically much smaller than $T$. We corroborate our theoretical findings with experiments on synthetic non-convex functions and on the real-world problem of hyper-parameter optimization, confirming the good practical performances of the proposed approach.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Approximate Bayesian Neural Operators: Uncertainty Quantification for Parametric PDEs

Neural operators are a type of deep architecture that learns to solve (i.e. learns the nonlinear solution operator of) partial differential equations (PDEs). The current state of the art for these models does not provide explicit uncertainty quantification. This is arguably even more of a problem for this kind of tasks than elsewhere in machine learning, because the dynamical systems typically described by PDEs often exhibit subtle, multiscale structure that makes errors hard to spot by humans. In this work, we first provide a mathematically detailed Bayesian formulation of the ''shallow'' (linear) version of neural operators in the formalism of Gaussian processes. We then extend this analytic treatment to general deep neural operators using approximate methods from Bayesian deep learning. We extend previous results on neural operators by providing them with uncertainty quantification. As a result, our approach is able to identify cases, and provide structured uncertainty estimates, where the neural operator fails to predict well.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Efficient Hyperparameter Tuning for Large Scale Kernel Ridge Regression

Kernel methods provide a principled approach to nonparametric learning. While their basic implementations scale poorly to large problems, recent advances showed that approximate solvers can efficiently handle massive datasets. A shortcoming of these solutions is that hyperparameter tuning is not taken care of, and left for the user to perform. Hyperparameters are crucial in practice and the lack of automated tuning greatly hinders efficiency and usability. In this paper, we work to fill in this gap focusing on kernel ridge regression based on the Nyström approximation. After reviewing and contrasting a number of hyperparameter tuning strategies, we propose a complexity regularization criterion based on a data dependent penalty, and discuss its efficient optimization. Then, we proceed to a careful and extensive empirical evaluation highlighting strengths and weaknesses of the different tuning strategies. Our analysis shows the benefit of the proposed approach, that we hence incorporate in a library for large scale kernel methods to derive adaptively tuned solutions.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Efficient Unsupervised Learning for Plankton Images

Monitoring plankton populations in situ is fundamental to preserve the aquatic ecosystem. Plankton microorganisms are in fact susceptible of minor environmental perturbations, that can reflect into consequent morphological and dynamical modifications. Nowadays, the availability of advanced automatic or semi-automatic acquisition systems has been allowing the production of an increasingly large amount of plankton image data. The adoption of machine learning algorithms to classify such data may be affected by the significant cost of manual annotation, due to both the huge quantity of acquired data and the numerosity of plankton species. To address these challenges, we propose an efficient unsupervised learning pipeline to provide accurate classification of plankton microorganisms. We build a set of image descriptors exploiting a two-step procedure. First, a Variational Autoencoder (VAE) is trained on features extracted by a pre-trained neural network. We then use the learnt latent space as image descriptor for clustering. We compare our method with state-of-the-art unsupervised approaches, where a set of pre-defined hand-crafted features is used for clustering of plankton images. The proposed pipeline outperforms the benchmark algorithms for all the plankton datasets included in our analysis, providing better image embedding properties.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Fast iterative regularization by reusing data

Discrete inverse problems correspond to solving a system of equations in a stable way with respect to noise in the data. A typical approach to enforce uniqueness and select a meaningful solution is to introduce a regularizer. While for most applications the regularizer is convex, in many cases it is not smooth nor strongly convex. In this paper, we propose and study two new iterative regularization methods, based on a primal-dual algorithm, to solve inverse problems efficiently. Our analysis, in the noise free case, provides convergence rates for the Lagrangian and the feasibility gap. In the noisy case, it provides stability bounds and early-stopping rules with theoretical guarantees. The main novelty of our work is the exploitation of some a priori knowledge about the solution set, i.e. redundant information. More precisely we show that the linear systems can be used more than once along the iteration. Despite the simplicity of the idea, we show that this procedure brings surprising advantages in the numerical applications. We discuss various approaches to take advantage of redundant information, that are at the same time consistent with our assumptions and flexible in the implementation. Finally, we illustrate our theoretical findings with numerical simulations for robust sparse recovery and image reconstruction through total variation. We confirm the efficiency of the proposed procedures, comparing the results with state-of-the-art methods.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

From Handheld to Unconstrained Object Detection: a Weakly-supervised On-line Learning Approach

Deep Learning (DL) based methods for object detection achieve remarkable performance at the cost of computationally expensive training and extensive data labeling. Robots embodiment can be exploited to mitigate this burden by acquiring automatically annotated training data via a natural interaction with a human showing the object of interest, handheld. However, learning solely from this data may introduce biases (the so-called domain shift), and prevents adaptation to novel tasks. While Weakly-supervised Learning (WSL) offers a well-established set of techniques to cope with these problems in general-purpose Computer Vision, its adoption in challenging robotic domains is still at a preliminary stage. In this work, we target the scenario of a robot trained in a teacher-learner setting to detect handheld objects. The aim is to improve detection performance in different settings by letting the robot explore the environment with a limited human labeling budget. We compare several techniques for WSL in detection pipelines to reduce model re-training costs without compromising accuracy, proposing solutions which target the considered robotic scenario. We show that the robot can improve adaptation to novel domains, either by interacting with a human teacher (Active Learning) or with an autonomous supervision (Semi-supervised Learning). We integrate our strategies into an on-line detection method, achieving efficient model update capabilities with few labels. We experimentally benchmark our method on challenging robotic object detection tasks under domain shift.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Iterative regularization for low complexity regularizers

Iterative regularization exploits the implicit bias of an optimization algorithm to regularize ill-posed problems. Constructing algorithms with such built-in regularization mechanisms is a classic challenge in inverse problems but also in modern machine learning, where it provides both a new perspective on algorithms analysis, and significant speed-ups compared to explicit regularization. In this work, we propose and study the first iterative regularization procedure able to handle biases described by non smooth and non strongly convex functionals, prominent in low-complexity regularization. Our approach is based on a primal-dual algorithm of which we analyze convergence and stability properties, even in the case where the original problem is unfeasible. The general results are illustrated considering the special case of sparse recovery with the $\ell_1$ penalty. Our theoretical results are complemented by experiments showing the computational benefits of our approach.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Mean Nyström Embeddings for Adaptive Compressive Learning

Compressive learning is an approach to efficient large scale learning based on sketching an entire dataset to a single mean embedding (the sketch), i.e. a vector of generalized moments. The learning task is then approximately solved as an inverse problem using an adapted parametric model. Previous works in this context have focused on sketches obtained by averaging random features, that while universal can be poorly adapted to the problem at hand. In this paper, we propose and study the idea of performing sketching based on data-dependent Nyström approximation. From a theoretical perspective we prove that the excess risk can be controlled under a geometric assumption relating the parametric model used to learn from the sketch and the covariance operator associated to the task at hand. Empirically, we show for k-means clustering and Gaussian modeling that for a fixed sketch size, Nyström sketches indeed outperform those built with random features.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Multiclass learning with margin: exponential rates with no bias-variance trade-off

We study the behavior of error bounds for multiclass classification under suitable margin conditions. For a wide variety of methods we prove that the classification error under a hard-margin condition decreases exponentially fast without any bias-variance trade-off. Different convergence rates can be obtained in correspondence of different margin assumptions. With a self-contained and instructive analysis we are able to generalize known results from the binary to the multiclass setting.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Nyström Kernel Mean Embeddings

Kernel mean embeddings are a powerful tool to represent probability distributions over arbitrary spaces as single points in a Hilbert space. Yet, the cost of computing and storing such embeddings prohibits their direct use in large-scale settings. We propose an efficient approximation procedure based on the Nyström method, which exploits a small random subset of the dataset. Our main result is an upper bound on the approximation error of this procedure. It yields sufficient conditions on the subsample size to obtain the standard $n^{-1/2}$ rate while reducing computational costs. We discuss applications of this result for the approximation of the maximum mean discrepancy and quadrature rules, and illustrate our theoretical findings with numerical experiments.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Optimal Rates for Spectral Algorithms with Least-Squares Regression over Hilbert Spaces

In this paper, we study regression problems over a separable Hilbert space with the square loss, covering non-parametric regression over a reproducing kernel Hilbert space. We investigate a class of spectral/regularized algorithms, including ridge regression, principal component regression, and gradient methods. We prove optimal, high-probability convergence results in terms of variants of norms for the studied algorithms, considering a capacity assumption on the hypothesis space and a general source condition on the target function. Consequently, we obtain almost sure convergence results with optimal rates. Our results improve and generalize previous results, filling a theoretical gap for the non-attainable cases.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Physics Informed Shallow Machine Learning for Wind Speed Prediction

The ability to predict wind is crucial for both energy production and weather forecasting. Mechanistic models that form the basis of traditional forecasting perform poorly near the ground. In this paper, we take an alternative data-driven approach based on supervised learning. We analyze a massive dataset of wind measured from anemometers located at 10 m height in 32 locations in two central and north west regions of Italy (Abruzzo and Liguria). We train supervised learning algorithms using the past history of wind to predict its value at a future time (horizon). Using data from a single location and time horizon we compare systematically several algorithms where we vary the input/output variables, the memory of the input and the linear vs non-linear learning model. We then compare performance of the best algorithms across all locations and forecasting horizons. We find that the optimal design as well as its performance vary with the location. We demonstrate that the presence of a reproducible diurnal cycle provides a rationale to understand this variation. We conclude with a systematic comparison with state of the art algorithms and show that, when the model is accurately designed, shallow algorithms are competitive with more complex deep architectures.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Scaling Gaussian Process Optimization by Evaluating a Few Unique Candidates Multiple Times

Computing a Gaussian process (GP) posterior has a computational cost cubical in the number of historical points. A reformulation of the same GP posterior highlights that this complexity mainly depends on how many \emph{unique} historical points are considered. This can have important implication in active learning settings, where the set of historical points is constructed sequentially by the learner. We show that sequential black-box optimization based on GPs (GP-Opt) can be made efficient by sticking to a candidate solution for multiple evaluation steps and switch only when necessary. Limiting the number of switches also limits the number of unique points in the history of the GP. Thus, the efficient GP reformulation can be used to exactly and cheaply compute the posteriors required to run the GP-Opt algorithms. This approach is especially useful in real-world applications of GP-Opt with high switch costs (e.g. switching chemicals in wet labs, data/model loading in hyperparameter optimization). As examples of this meta-approach, we modify two well-established GP-Opt algorithms, GP-UCB and GP-EI, to switch candidates as infrequently as possible adapting rules from batched GP-Opt. These versions preserve all the theoretical no-regret guarantees while improving practical aspects of the algorithms such as runtime, memory complexity, and the ability of batching candidates and evaluating them in parallel.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

Asymptotics of Ridge (less) Regression under General Source Condition

We analyze the prediction error of ridge regression in an asymptotic regime where the sample size and dimension go to infinity at a proportional rate. In particular, we consider the role played by the structure of the true regression parameter. We observe that the case of a general deterministic parameter can be reduced to the case of a random parameter from a structured prior. The latter assumption is a natural adaptation of classic smoothness assumptions in nonparametric regression, which are known as source conditions in the the context of regularization theory for inverse problems. Roughly speaking, we assume the large coefficients of the parameter are in correspondence to the principal components. In this setting a precise characterisation of the test error is obtained, depending on the inputs covariance and regression parameter structure. We illustrate this characterisation in a simplified setting to investigate the influence of the true parameter on optimal regularisation for overparameterized models. We show that interpolation (no regularisation) can be optimal even with bounded signal-to-noise ratio (SNR), provided that the parameter coefficients are larger on high-variance directions of the data, corresponding to a more regular function than posited by the regularization term. This contrasts with previous work considering ridge regression with isotropic prior, in which case interpolation is only optimal in the limit of infinite SNR.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

Construction and Monte Carlo estimation of wavelet frames generated by a reproducing kernel

We introduce a construction of multiscale tight frames on general domains. The frame elements are obtained by spectral filtering of the integral operator associated with a reproducing kernel. Our construction extends classical wavelets as well as generalized wavelets on both continuous and discrete non-Euclidean structures such as Riemannian manifolds and weighted graphs. Moreover, it allows to study the relation between continuous and discrete frames in a random sampling regime, where discrete frames can be seen as Monte Carlo estimates of the continuous ones. Pairing spectral regularization with learning theory, we show that a sample frame tends to its population counterpart, and derive explicit finite-sample rates on spaces of Sobolev and Besov regularity. Our results prove the stability of frames constructed on empirical data, in the sense that all stochastic discretizations have the same underlying limit regardless of the set of initial training samples.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

A General Framework for Consistent Structured Prediction with Implicit Loss Embeddings

We propose and analyze a novel theoretical and algorithmic framework for structured prediction. While so far the term has referred to discrete output spaces, here we consider more general settings, such as manifolds or spaces of probability measures. We define structured prediction as a problem where the output space lacks a vectorial structure. We identify and study a large class of loss functions that implicitly defines a suitable geometry on the problem. The latter is the key to develop an algorithmic framework amenable to a sharp statistical analysis and yielding efficient computations. When dealing with output spaces with infinite cardinality, a suitable implicit formulation of the estimator is shown to be crucial.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Decentralised Learning with Random Features and Distributed Gradient Descent

We investigate the generalisation performance of Distributed Gradient Descent with Implicit Regularisation and Random Features in the homogenous setting where a network of agents are given data sampled independently from the same unknown distribution. Along with reducing the memory footprint, Random Features are particularly convenient in this setting as they provide a common parameterisation across agents that allows to overcome previous difficulties in implementing Decentralised Kernel Regression. Under standard source and capacity assumptions, we establish high probability bounds on the predictive performance for each agent as a function of the step size, number of iterations, inverse spectral gap of the communication matrix and number of Random Features. By tuning these parameters, we obtain statistical rates that are minimax optimal with respect to the total number of samples in the network. The algorithm provides a linear improvement over single machine Gradient Descent in memory cost and, when agents hold enough data with respect to the network size and inverse spectral gap, a linear speed-up in computational runtime for any network topology. We present simulations that show how the number of Random Features, iterations and samples impact predictive performance.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Hyperbolic Manifold Regression

Geometric representation learning has recently shown great promise in several machine learning settings, ranging from relational learning to language processing and generative models. In this work, we consider the problem of performing manifold-valued regression onto an hyperbolic space as an intermediate component for a number of relevant machine learning applications. In particular, by formulating the problem of predicting nodes of a tree as a manifold regression task in the hyperbolic space, we propose a novel perspective on two challenging tasks: 1) hierarchical classification via label embeddings and 2) taxonomy extension of hyperbolic representations. To address the regression problem we consider previous methods as well as proposing two novel approaches that are computationally more advantageous: a parametric deep learning model that is informed by the geodesics of the target space and a non-parametric kernel-method for which we also prove excess risk bounds. Our experiments show that the strategy of leveraging the hyperbolic geometry is promising. In particular, in the taxonomy expansion setting, we find that the hyperbolic-based estimators significantly outperform methods performing regression in the ambient Euclidean space.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Near-linear Time Gaussian Process Optimization with Adaptive Batching and Resparsification

Gaussian processes (GP) are one of the most successful frameworks to model uncertainty. However, GP optimization (e.g., GP-UCB) suffers from major scalability issues. Experimental time grows linearly with the number of evaluations, unless candidates are selected in batches (e.g., using GP-BUCB) and evaluated in parallel. Furthermore, computational cost is often prohibitive since algorithms such as GP-BUCB require a time at least quadratic in the number of dimensions and iterations to select each batch. In this paper, we introduce BBKB (Batch Budgeted Kernel Bandits), the first no-regret GP optimization algorithm that provably runs in near-linear time and selects candidates in batches. This is obtained with a new guarantee for the tracking of the posterior variances that allows BBKB to choose increasingly larger batches, improving over GP-BUCB. Moreover, we show that the same bound can be used to adaptively delay costly updates to the sparse GP approximation used by BBKB, achieving a near-constant per-step amortized cost. These findings are then confirmed in several experiments, where BBKB is much faster than state-of-the-art methods.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Theory III: Dynamics and Generalization in Deep Networks

The key to generalization is controlling the complexity of the network. However, there is no obvious control of complexity -- such as an explicit regularization term -- in the training of deep networks for classification. We will show that a classical form of norm control -- but kind of hidden -- is present in deep networks trained with gradient descent techniques on exponential-type losses. In particular, gradient descent induces a dynamics of the normalized weights which converge for $t \to \infty$ to an equilibrium which corresponds to a minimum norm (or maximum margin) solution. For sufficiently large but finite $ρ$ -- and thus finite $t$ -- the dynamics converges to one of several margin maximizers, with the margin monotonically increasing towards a limit stationary point of the flow. In the usual case of stochastic gradient descent, most of the stationary points are likely to be convex minima corresponding to a constrained minimizer -- the network with normalized weights-- which corresponds to vanishing regularization. The solution has zero generalization gap, for fixed architecture, asymptotically for $N \to \infty$, where $N$ is the number of training examples. Our approach extends some of the original results of Srebro from linear networks to deep networks and provides a new perspective on the implicit bias of gradient descent. We believe that the elusive complexity control we describe is responsible for the puzzling empirical finding of good predictive performance by deep networks, despite overparametrization.

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preprint2019arXiv

Monte Carlo wavelets: a randomized approach to frame discretization

In this paper we propose and study a family of continuous wavelets on general domains, and a corresponding stochastic discretization that we call Monte Carlo wavelets. First, using tools from the theory of reproducing kernel Hilbert spaces and associated integral operators, we define a family of continuous wavelets by spectral calculus. Then, we propose a stochastic discretization based on Monte Carlo estimates of integral operators. Using concentration of measure results, we establish the convergence of such a discretization and derive convergence rates under natural regularity assumptions.

0 citations0 reviewsNo code linkedOpen access