A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Study optimal portfolio management with periodic evaluations in stochastic models, considering convex constraints.
problem Optimal portfolio management under ratio-type periodic evaluations in stochastic factor models with convex trading constraints.
method Transformed infinite horizon optimal control problem into an auxiliary terminal wealth optimization problem. Introduced an auxiliary unconstrained optimization problem in a modified market model. Used martingale duality approach to establish dual minimizer and optimal unconstrained wealth process.
result Derived and verified the optimal constrained portfolio process for the original problem over an infinite horizon.
Wide neural networks with weight decay exhibit neural collapse.
problem Proving neural collapse in wide neural networks trained with weight decay.
method Generic guarantees on neural collapse for wide networks with weight decay, proving low training error and balancedness, and bounded conditioning.
result First proof of neural collapse in end-to-end training of wide neural networks with weight decay.
We consider a variant of online convex optimization in which both the instances (input vectors) and the comparator (weight vector) are unconstrained. We exploit a natural scale invariance symmetry in our unconstrained setting: the predictions of the optimal comparator are invariant under any linear transformation of th…
Paper explains neural collapse in neural networks using a new model.
problem Understanding neural collapse in neural networks during training.
method Introducing the unconstrained layer-peeled model (ULPM) to prove gradient flow convergence to critical points of a minimum-norm separation problem.
result Proves that all critical points are strict saddle points except the global minimizers exhibiting neural collapse.
Obtaining compact and discriminative features is one of the major challenges in many of the real-world image classification tasks such as face verification and object recognition. One possible approach is to represent input image on the basis of high-level features that carry semantic meaning which humans can understan…
Despite significant progress made over the past twenty five years, unconstrained face verification remains a challenging problem. This paper proposes an approach that couples a deep CNN-based approach with a low-dimensional discriminative embedding learned using triplet probability constraints to solve the unconstraine…
Tree ensemble kernels improve Bayesian optimization for mixed features and constraints.
problem Optimizing over mixed-feature spaces with known constraints.
method Kernel interpretation of tree ensembles as Gaussian Process prior, compatible optimization formulation for acquisition function, integration of known constraints.
result Framework outperforms state-of-the-art methods for mixed-feature spaces and constraints.
Low rank matrix factorisation is often used in recommender systems as a way of extracting latent features. When dealing with large and sparse datasets, traditional recommendation algorithms face the problem of acquiring large, unrestrained, fluctuating values over predictions especially for users/items with very few co…
We clarify what fairness guarantees we can and cannot expect to follow from unconstrained machine learning. Specifically, we characterize when unconstrained learning on its own implies group calibration, that is, the outcome variable is conditionally independent of group membership given the score. We show that under r…
Neural collapse occurs in normalized features over a Riemannian manifold.
problem Understanding neural collapse in normalized feature models.
method Simplified multi-class classification task to a nonconvex optimization problem over the Riemannian manifold, analyzing the landscape of critical points.
result The only global minimizers are neural collapse solutions, with all other critical points being strict saddles.
Recurrent neural networks can be large and compute-intensive, yet many applications that benefit from RNNs run on small devices with very limited compute and storage capabilities while still having run-time constraints. As a result, there is a need for compression techniques that can achieve significant compression wit…
For technology (like serious games) that aims to deliver interactive learning, it is important to address relevant mental experiences such as reflective thinking during problem solving. To facilitate research in this direction, we present the weDraw-1 Movement Dataset of body movement sensor data and reflective thinkin…
A novel method for common and individual feature analysis from exceedingly large-scale data is proposed, in order to ensure the tractability of both the computation and storage and thus mitigate the curse of dimensionality, a major bottleneck in modern data science. This is achieved by making use of the inherent redund…
A drawdown constraint forces the current wealth to remain above a given function of its maximum to date. We consider the portfolio optimisation problem of maximising the long-term growth rate of the expected utility of wealth subject to a drawdown constraint, as in the original setup of Grossman and Zhou (1993). We wor…
Gaussian process (GP) modulated Cox processes are widely used to model point patterns. Existing approaches require a mapping (link function) between the unconstrained GP and the positive intensity function. This commonly yields solutions that do not have a closed form or that are restricted to specific covariance funct…
Develops methods for estimating constrained function-valued parameters in infinite-dimensional models.
problem Estimating function-valued parameters with structural constraints in complex models.
method Characterizes constrained solutions as minimizers of penalized population risk, using a Lagrange-type formulation and path through unconstrained space.
result Proposes estimators that achieve optimal risk and constraint satisfaction, applicable across various statistical learning approaches.