Related papers: On the trade-off between complexity and correlatio…
Empirical studies suggest that machine learning models often rely on features, such as the background, that may be spuriously correlated with the label only during training time, resulting in poor accuracy during test-time. In this work, we…
We introduce a simple analysis of the structural complexity of infinite-memory processes built from random samples of stationary, ergodic finite-memory component processes. Such processes are familiar from the well known multi-arm Bandit…
This paper investigates a new learning formulation called structured sparsity, which is a natural extension of the standard sparsity concept in statistical learning and compressive sensing. By allowing arbitrary structures on the feature…
Many algorithms for processing probabilistic networks are dependent on the topological properties of the problem's structure. Such algorithms (e.g., clustering, conditioning) are effective only if the problem has a sparse graph captured by…
In computer simulation of the learning process is usually assumed that all elements of the training material are assimilated equally durable. But in practice, the knowledge, which a student uses in its operations, are remembered much…
We propose a method to find out the community structure of a complex network. In this method the ground state problem of a ferromagnetic random field Ising model is considered on the network with the magnetic field $B_s = +\infty$, $B_{t} =…
The autocorrelation values of two classes of binary sequences are shown to be good in [6]. We study the 2-adic complexity of these sequences. Our results show that the 2-adic complexity of such sequences is large enough to resist the attack…
Correlations between two variables of a high-dimensional system can be indicative of an underlying interaction, but can also result from indirect effects. Inverse Ising inference is a method to distinguish one from the other. Essentially,…
We consider the problem of structure learning for linear causal models based on observational data. We treat models given by possibly cyclic mixed graphs, which allow for feedback loops and effects of latent confounders. Generalizing…
A new type of collective excitations, due exclusively to the topology of a complex random network that can be characterized by a fractal dimension $D_F$, is investigated. We show analytically that these excitations generate phase…
Neural networks are known to be highly sensitive to adversarial examples. These may arise due to different factors, such as random initialization, or spurious correlations in the learning problem. To better understand these factors, we…
When training autoregressive models to forecast dynamical systems, a critical question arises: how far into the future should the model be trained to predict? Too short a horizon may miss long-term trends, while too long a horizon can…
We present a cascading failure model of two interdependent networks in which functional nodes belong to components of size greater than or equal to $s$. We find theoretically and via simulation that in complex networks with random…
The Ising model was originally developed to model magnetisation of solids in statistical physics. As a network of binary variables with the probability of becoming 'active' depending only on direct neighbours, the Ising model appears…
Empirical process theory for i.i.d. observations has emerged as a ubiquitous tool for understanding the generalization properties of various statistical problems. However, in many applications where the data exhibit temporal dependencies…
We consider the problem of sequential prediction and provide tools to study the minimax value of the associated game. Classical statistical learning theory provides several useful complexity measures to study learning with i.i.d. data. Our…
Continual learning has become a trending topic in machine learning. Recent studies have discovered an interesting phenomenon called loss of plasticity, referring to neural networks gradually losing the ability to learn new tasks. However,…
Deep Learning models have shown success in a large variety of tasks by extracting correlation patterns from high-dimensional data but still struggle when generalizing out of their initial distribution. As causal engines aim to learn…
We perform a numerical study of the long range (LR) ferromagnetic Ising model with power law decaying interactions ($J \propto r^{-d-\sigma}$) both on a one-dimensional chain ($d=1$) and on a square lattice ($d=2$). We use advanced cluster…
Studying the reliability of complex systems using machine learning techniques involves facing a series of technical and practical challenges, ranging from the intrinsic nature of the system and data to the difficulties in modeling and…