Alexander Y. Shestopaloff

Gerardo Duran-Martin, Leandro Sánchez-Betancourt, Alexander Y. Shestopaloff et al.

We propose a unifying framework for methods that perform probabilistic online learning in non-stationary environments. We call the framework BONE, which stands for generalised (B)ayesian (O)nline learning in (N)on-stationary (E)nvironments. BONE provides a common structure to tackle a variety of problems, including online continual learning, prequential forecasting, and contextual bandits. The framework requires specifying three modelling choices: (i) a model for measurements (e.g., a neural network), (ii) an auxiliary process to model non-stationarity (e.g., the time since the last changepoint), and (iii) a conditional prior over model parameters (e.g., a multivariate Gaussian). The framework also requires two algorithmic choices, which we use to carry out approximate inference under this framework: (i) an algorithm to estimate beliefs (posterior distribution) about the model parameters given the auxiliary variable, and (ii) an algorithm to estimate beliefs about the auxiliary variable. We show how the modularity of our framework allows for many existing methods to be reinterpreted as instances of BONE, and it allows us to propose new methods. We compare experimentally existing methods with our proposed new method on several datasets, providing insights into the situations that make each method more suitable for a specific task. We provide a Jax open source library to facilitate the adoption of this framework.

Taurai Muvunza, Egor Kraev, Pere Planell-Morell et al.

Existing feature filters rely on statistical pair-wise dependence metrics to model feature-target relationships, but this approach may fail when the target depends on higher-order feature interactions rather than individual contributions. We introduce Mutual Information Neural Estimation Regularized Vetting Algorithm (MINERVA), a novel approach to supervised feature selection based on neural estimation of mutual information between features and targets. We paramaterize the approximation of mutual information with neural networks and perform feature selection using a carefully designed loss function augmented with sparsity-inducing regularizers. Our method is implemented in a two-stage process to decouple representation learning from feature selection, ensuring better generalization and a more accurate expression of feature importance. We present examples of ubiquitous dependency structures that are rarely captured in literature and show that our proposed method effectively captures these complex feature-target relationships by evaluating feature subsets as an ensemble. Experimental results on synthetic and real-life fraud datasets demonstrate the efficacy of our method and its ability to perform exact solutions.

Zichuan Guo, Mihai Cucuringu, Alexander Y. Shestopaloff

We tackle the challenges of modeling high-dimensional data sets, particularly those with latent low-dimensional structures hidden within complex, non-linear, and noisy relationships. Our approach enables a seamless integration of concepts from non-parametric regression, factor models, and neural networks for high-dimensional regression. Our approach introduces PCA and Soft PCA layers, which can be embedded at any stage of a neural network architecture, allowing the model to alternate between factor modeling and non-linear transformations. This flexibility makes our method especially effective for processing hierarchical compositional data. We explore ours and other techniques for imposing low-rank structures on neural networks and examine how architectural design impacts model performance. The effectiveness of our method is demonstrated through simulation studies, as well as applications to forecasting future price movements of equity ETF indices and nowcasting with macroeconomic data.

Gerardo Duran-Martin, Matias Altamirano, Alexander Y. Shestopaloff et al.

We derive a novel, provably robust, and closed-form Bayesian update rule for online filtering in state-space models in the presence of outliers and misspecified measurement models. Our method combines generalised Bayesian inference with filtering methods such as the extended and ensemble Kalman filter. We use the former to show robustness and the latter to ensure computational efficiency in the case of nonlinear models. Our method matches or outperforms other robust filtering methods (such as those based on variational Bayes) at a much lower computational cost. We show this empirically on a range of filtering problems with outlier measurements, such as object tracking, state estimation in high-dimensional chaotic systems, and online learning of neural networks.

Yichi Zhang, Mihai Cucuringu, Alexander Y. Shestopaloff et al.

In multivariate time series systems, key insights can be obtained by discovering lead-lag relationships inherent in the data, which refer to the dependence between two time series shifted in time relative to one another, and which can be leveraged for the purposes of control, forecasting or clustering. We develop a clustering-driven methodology for robust detection of lead-lag relationships in lagged multi-factor models. Within our framework, the envisioned pipeline takes as input a set of time series, and creates an enlarged universe of extracted subsequence time series from each input time series, via a sliding window approach. This is then followed by an application of various clustering techniques, (such as k-means++ and spectral clustering), employing a variety of pairwise similarity measures, including nonlinear ones. Once the clusters have been extracted, lead-lag estimates across clusters are robustly aggregated to enhance the identification of the consistent relationships in the original universe. We establish connections to the multireference alignment problem for both the homogeneous and heterogeneous settings. Since multivariate time series are ubiquitous in a wide range of domains, we demonstrate that our method is not only able to robustly detect lead-lag relationships in financial markets, but can also yield insightful results when applied to an environmental data set.