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We present a unified information-theoretic framework elucidating the interplay between stability, privacy, and the generalization performance of quantum learning algorithms. We establish a bound on the expected generalization error in terms…

We say that an algorithm is stable if small changes in the input result in small changes in the output. This kind of algorithm stability is particularly relevant when analyzing and visualizing time-varying data. Stability in general plays…

A crucial assumption in most statistical learning theory is that samples are independently and identically distributed (i.i.d.). However, for many real applications, the i.i.d. assumption does not hold. We consider learning problems in…

Stochastic optimization has found wide applications in minimizing objective functions in machine learning, which motivates a lot of theoretical studies to understand its practical success. Most of existing studies focus on the convergence…

Training modern neural networks often relies on large learning rates, operating at the edge of stability, where the optimization dynamics exhibit oscillatory and chaotic behavior. Empirically, this regime often yields improved…

Recently, a framework for controller design of sampled-data nonlinear systems via their approximate discrete-time models has been proposed in the literature. In this paper we develop novel tools that can be used within this framework and…

(Stochastic) bilevel optimization is a frequently encountered problem in machine learning with a wide range of applications such as meta-learning, hyper-parameter optimization, and reinforcement learning. Most of the existing studies on…

Incremental learning from non-stationary data poses special challenges to the field of machine learning. Although new algorithms have been developed for this, assessment of results and comparison of behaviors are still open problems, mainly…

We study which machine learning algorithms have tight generalization bounds. First, we present conditions that preclude the existence of tight generalization bounds. Specifically, we show that algorithms that have certain inductive biases…

Stacking is a general approach for combining multiple models toward greater predictive accuracy. It has found various application across different domains, ensuing from its meta-learning nature. Our understanding, nevertheless, on how and…

A common problem to all applications of linear finite dynamical systems is analyzing the dynamics without enumerating every possible state transition. Of particular interest is the long term dynamical behaviour. In this paper, we study the…

The present paper provides a new generic strategy leading to non-asymptotic theoretical guarantees on the Leave-one-Out procedure applied to a broad class of learning algorithms. This strategy relies on two main ingredients: the new notion…

In machine learning we often encounter structured output prediction problems (SOPPs), i.e. problems where the output space admits a rich internal structure. Application domains where SOPPs naturally occur include natural language…

While adversarial robustness and generalization have individually received substantial attention in the recent literature on quantum machine learning, their interplay is much less explored. In this chapter, we address this interplay for…

Hypothesis transfer learning (HTL) contrasts domain adaptation by allowing for a previous task leverage, named the source, into a new one, the target, without requiring access to the source data. Indeed, HTL relies only on a hypothesis…

As deep neural networks are highly expressive, it is important to find solutions with small generalization gap (the difference between the performance on the training data and unseen data). Focusing on the stochastic nature of training, we…

We investigate the generalizability of learned binary relations: functions that map pairs of instances to a logical indicator. This problem has application in numerous areas of machine learning, such as ranking, entity resolution and link…

Existing analyses of neural network training often operate under the unrealistic assumption of an extremely small learning rate. This lies in stark contrast to practical wisdom and empirical studies, such as the work of J. Cohen et al.…

In this work, the probability of an event under some joint distribution is bounded by measuring it with the product of the marginals instead (which is typically easier to analyze) together with a measure of the dependence between the two…

Recent advances in learning for control allow to synthesize vehicle controllers from learned system dynamics and maintain robust stability guarantees. However, no approach is well-suited for training linear time-invariant (LTI) controllers…