Stochastic gradient descent (SGD) is one of the most popular algorithms in modern machine learning. The noise encountered in these applications is different from that in many theoretical analyses of stochastic gradient algorithms. In this article, we discuss some of the common properties of energy landscapes and stochastic noise encountered in machine learning problems, and how they affect SGD-based optimization. In particular, we show that the learning rate in SGD with machine learning noise can be chosen to be small, but uniformly positive for all times if the energy landscape resembles that of overparametrized deep learning problems. If the objective function satisfies a Lojasiewicz inequality, SGD converges to the global minimum exponentially fast, and even for functions which may have local minima, we establish almost sure convergence to the global minimum at an exponential rate from any finite energy initialization. The assumptions that we make in this result concern the behavior where the objective function is either small or large and the nature of the gradient noise, but the energy landscape is fairly unconstrained on the domain where the objective function takes values in an intermediate regime.

Finding the optimal hyperparameters of a model can be cast as a bilevel optimization problem, typically solved using zero-order techniques. In this work we study first-order methods when the inner optimization problem is convex but non-smooth. We show that the forward-mode differentiation of proximal gradient descent and proximal coordinate descent yield sequences of Jacobians converging toward the exact Jacobian. Using implicit differentiation, we show it is possible to leverage the non-smoothness of the inner problem to speed up the computation. Finally, we provide a bound on the error made on the hypergradient when the inner optimization problem is solved approximately. Results on regression and classification problems reveal computational benefits for hyperparameter optimization, especially when multiple hyperparameters are required.

We consider a rank regression setting, in which a dataset of $N$ samples with features in $\mathbb{R}^d$ is ranked by an oracle via $M$ pairwise comparisons. Specifically, there exists a latent total ordering of the samples; when presented with a pair of samples, a noisy oracle identifies the one ranked higher with respect to the underlying total ordering. A learner observes a dataset of such comparisons and wishes to regress sample ranks from their features. We show that to learn the model parameters with $\epsilon > 0$ accuracy, it suffices to conduct $M \in \Omega(dN\log^3 N/\epsilon^2)$ comparisons uniformly at random when $N$ is $\Omega(d/\epsilon^2)$.

We assess the demand effects of discounts on train tickets issued by the Swiss Federal Railways, the so-called `supersaver tickets', based on machine learning, a subfield of artificial intelligence. Considering a survey-based sample of buyers of supersaver tickets, we investigate which customer- or trip-related characteristics (including the discount rate) predict buying behavior, namely: booking a trip otherwise not realized by train, buying a first- rather than second-class ticket, or rescheduling a trip (e.g.\ away from rush hours) when being offered a supersaver ticket. Predictive machine learning suggests that customer's age, demand-related information for a specific connection (like departure time and utilization), and the discount level permit forecasting buying behavior to a certain extent. Furthermore, we use causal machine learning to assess the impact of the discount rate on rescheduling a trip, which seems relevant in the light of capacity constraints at rush hours. Assuming that (i) the discount rate is quasi-random conditional on our rich set of characteristics and (ii) the buying decision increases weakly monotonically in the discount rate, we identify the discount rate's effect among `always buyers', who would have traveled even without a discount, based on our survey that asks about customer behavior in the absence of discounts. We find that on average, increasing the discount rate by one percentage point increases the share of rescheduled trips by 0.16 percentage points among always buyers. Investigating effect heterogeneity across observables suggests that the effects are higher for leisure travelers and during peak hours when controlling several other characteristics.

This paper shows that graph spectral embedding using the random walk Laplacian produces vector representations which are completely corrected for node degree. Under a generalised random dot product graph, the embedding provides uniformly consistent estimates of degree-corrected latent positions, with asymptotically Gaussian error. In the special case of a degree-corrected stochastic block model, the embedding concentrates about K distinct points, representing communities. These can be recovered perfectly, asymptotically, through a subsequent clustering step, without spherical projection, as commonly required by algorithms based on the adjacency or normalised, symmetric Laplacian matrices. While the estimand does not depend on degree, the asymptotic variance of its estimate does -- higher degree nodes are embedded more accurately than lower degree nodes. Our central limit theorem therefore suggests fitting a weighted Gaussian mixture model as the subsequent clustering step, for which we provide an expectation-maximisation algorithm.

We tackle object category discovery, which is the problem of discovering and localizing novel objects in a large unlabeled dataset. While existing methods show results on datasets with less cluttered scenes and fewer object instances per image, we present our results on the challenging COCO dataset. Moreover, we argue that, rather than discovering new categories from scratch, discovery algorithms can benefit from identifying what is already known and focusing their attention on the unknown. We propose a method to use prior knowledge about certain object categories to discover new categories by leveraging two memory modules, namely Working and Semantic memory. We show the performance of our detector on the COCO minival dataset to demonstrate its in-the-wild capabilities.

Along with the rapid expansion of information technology and digitalization of health data, there is an increasing concern on maintaining data privacy while garnering the benefits in medical field. Two critical challenges are identified: Firstly, medical data is naturally distributed across multiple local sites, making it difficult to collectively train machine learning models without data leakage. Secondly, in medical applications, data are often collected from different sources and views, resulting in heterogeneity and complexity that requires reconciliation. This paper aims to provide a generic Federated Multi-View Learning (FedMV) framework for multi-view data leakage prevention, which is based on different types of local data availability and enables to accommodate two types of problems: Vertical Federated Multi-View Learning (V-FedMV) and Horizontal Federated Multi-View Learning (H-FedMV). We experimented with real-world keyboard data collected from BiAffect study. The results demonstrated that the proposed FedMV approach can make full use of multi-view data in a privacy-preserving way, and both V-FedMV and H-FedMV methods perform better than their single-view and pairwise counterparts. Besides, the proposed model can be easily adapted to deal with multi-view sequential data in a federated environment, which has been modeled and experimentally studied. To the best of our knowledge, this framework is the first to consider both vertical and horizontal diversification in the multi-view setting, as well as their sequential federated learning.

Attempts of studying implicit regularization associated to gradient descent (GD) have identified matrix completion as a suitable test-bed. Late findings suggest that this phenomenon cannot be phrased as a minimization-norm problem, implying that a paradigm shift is required and that dynamics has to be taken into account. In the present work we address the more general setup of tensor completion by leveraging two popularized tensor factorization, namely Tucker and TensorTrain (TT). We track relevant quantities such as tensor nuclear norm, effective rank, generalized singular values and we introduce deep Tucker and TT unconstrained factorization to deal with the completion task. Experiments on both synthetic and real data show that gradient descent promotes solution with low-rank, and validate the conjecture saying that the phenomenon has to be addressed from a dynamical perspective.

Aquatic organisms involved in predator-prey interactions perform impressive feats of fluid manipulation to enhance their chances of survival [1-8]. Since early studies where prey fish were reported to rapidly accelerate from rest by bending into a C-shape and unfurling their tail [9-12], impulsive locomotion patterns have been the subject of intense investigation. Studying escape strategies of prey fish has led to the discovery of sensing mechanisms [13-15], dedicated neural circuits [16-19], and bio-mechanic principles [20, 21]. From the perspective of hydrodynamics, several studies have sought to understand the C-start escape response and how it imparts momentum to the surrounding fluid [22-27]. However, experiments and observations indicate that swimming escapes can take a variety of forms. For example, after the initial burst from rest, many fish are seen coasting instead of swimming continuously [11, 28, 29]. Furthermore, theoretical [30-32] as well as experimental [33] studies have suggested that intermittent swimming styles, termed burst-coast swimming, can be more efficient than continuous swimming when maximizing distance given a fixed amount of energy. This raises the question of when and why different swimming escape patterns are employed in nature, and which biophysical cost functions they optimize. Given a cost function, reverse engineering methodologies have been employed to identify links to resulting swimming patterns e.g.

Understanding how information propagates in real-life complex networks yields a better understanding of dynamic processes such as misinformation or epidemic spreading. The recently introduced branch of machine learning methods for learning node representations offers many novel applications, one of them being the task of spreading prediction addressed in this paper. We explore the utility of the state-of-the-art node representation learners when used to assess the effects of spreading from a given node, estimated via extensive simulations. Further, as many real-life networks are topologically similar, we systematically investigate whether the learned models generalize to previously unseen networks, showing that in some cases very good model transfer can be obtained. This work is one of the first to explore transferability of the learned representations for the task of node regression; we show there exist pairs of networks with similar structure between which the trained models can be transferred (zero-shot), and demonstrate their competitive performance. To our knowledge, this is one of the first attempts to evaluate the utility of zero-shot transfer for the task of node regression.