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Online Passive-Aggressive (PA) learning is a class of online margin-based algorithms suitable for a wide range of real-time prediction tasks, including classification and regression. PA algorithms are formulated in terms of deterministic…
Constructing an efficient parameterization of a large, noisy data set of points lying close to a smooth manifold in high dimension remains a fundamental problem. One approach consists in recovering a local parameterization using the local…
Independent component analysis (ICA) is popular in many applications, including cognitive neuroscience and signal processing. Due to computational constraints, principal component analysis is used for dimension reduction prior to ICA…
Most real-world problems that machine learning algorithms are expected to solve face the situation with 1) unknown data distribution; 2) little domain-specific knowledge; and 3) datasets with limited annotation. We propose Non-Parametric…
Anomalies are samples that significantly deviate from the rest of the data and their detection plays a major role in building machine learning models that can be reliably used in applications such as data-driven design and novelty…
Constructing good representations is critical for learning complex tasks in a sample efficient manner. In the context of meta-learning, representations can be constructed from common patterns of previously seen tasks so that a future task…
Subspace clustering aims to group data points into multiple clusters of which each corresponds to one subspace. Most existing subspace clustering approaches assume that input data lie on linear subspaces. In practice, however, this…
The high-dimensional data setting, in which p >> n, is a challenging statistical paradigm that appears in many real-world problems. In this setting, learning a compact, low-dimensional representation of the data can substantially help…
Linear regression studies the problem of estimating a model parameter $\beta^* \in \mathbb{R}^p$, from $n$ observations $\{(y_i,\mathbf{x}_i)\}_{i=1}^n$ from linear model $y_i = \langle \mathbf{x}_i,\beta^* \rangle + \epsilon_i$. We…
Despite a lack of theoretical understanding, deep neural networks have achieved unparalleled performance in a wide range of applications. On the other hand, shallow representation learning with component analysis is associated with rich…
We propose a novel unsupervised framework for \emph{Invariant Risk Minimization} (IRM), extending the concept of invariance to settings where labels are unavailable. Traditional IRM methods rely on labeled data to learn representations that…
Machine learning (ML) methods have proved to be a very successful tool in physical sciences, especially when applied to experimental data analysis. Artificial intelligence is particularly good at recognizing patterns in high dimensional…
Methodologies for multidimensionality reduction aim at discovering low-dimensional manifolds where data ranges. Principal Component Analysis (PCA) is very effective if data have linear structure. But fails in identifying a possible…
For a linear system, the response to a stimulus is often superposed by its responses to other decomposed stimuli. In quantum mechanics, a state is the superposition of multiple eigenstates. Here, by taking advantage of the phase difference,…
In recent years, Artificial Intelligence techniques have proved to be very successful when applied to problems in physical sciences. Here we apply an unsupervised Machine Learning (ML) algorithm called Principal Component Analysis (PCA) as…
We study the problem of learning mixtures of low-rank models, i.e. reconstructing multiple low-rank matrices from unlabelled linear measurements of each. This problem enriches two widely studied settings -- low-rank matrix sensing and mixed…
We demonstrate the utility of an unsupervised machine learning tool for the detection of phase transitions in off-lattice systems. We focus on the application of principal component analysis (PCA) to detect the freezing transitions of…
Principal component analysis (PCA) is a key tool in the field of data dimensionality reduction. However, some applications involve heterogeneous data that vary in quality due to noise characteristics associated with each data sample.…
The autoencoder is an artificial neural network model that learns hidden representations of unlabeled data. With a linear transfer function it is similar to the principal component analysis (PCA). While both methods use weight vectors for…
As far as the identification of linear time-invariant state-space representation is concerned, among all of the solutions available in the literature, the subspace-based state-space model identification techniques have proved their…