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.
Algebraic treatment of connection reduction over a special disc.
We consider active maximum a posteriori (MAP) inference problem for Hidden Markov Models (HMM), where, given an initial MAP estimate of the hidden sequence, we select to label certain states in the sequence to improve the estimation accuracy of the remaining states. We develop an analytical approach to this problem for…
We investigate the Kaluza-Klein reductions to ten dimensions of the purely gravitational half-BPS M-theory backgrounds: the M-wave and the Kaluza-Klein monopole. We determine the moduli space of smooth (supersymmetric) Kaluza-Klein reductions by classifying the freely-acting spacelike Killing vectors which preserve som…
Optimal persuasion involves projecting state vectors onto lower-dimensional 'optimal information manifolds'.
In this paper, we first study the Poisson reductions of controlled Hamiltonian (CH) system and symmetric CH system by controllability distributions. These reductions are the extension of Poisson reductions by distribution for Poisson manifolds to that for phase spaces of CH systems with external force and control. We g…
Dictionary leaning (DL) and dimensionality reduction (DR) are powerful tools to analyze high-dimensional noisy signals. This paper presents a proposal of a novel Riemannian joint dimensionality reduction and dictionary learning (R-JDRDL) on symmetric positive definite (SPD) manifolds for classification tasks. The joint…
Modeling data as being sampled from a union of independent subspaces has been widely applied to a number of real world applications. However, dimensionality reduction approaches that theoretically preserve this independence assumption have not been well studied. Our key contribution is to show that projection vect…
Policy gradient methods have demonstrated success in reinforcement learning tasks that have high-dimensional continuous state and action spaces. However, policy gradient methods are also notoriously sample inefficient. This can be attributed, at least in part, to the high variance in estimating the gradient of the task…
RC flow learns molecular kinetics in low dimensions.
Reduces nonlinear electromechanical dynamics through quasi-steady state hypothesis.
POTD estimates SDR subspace using optimal transport for binary response.
Sequential or online dimensional reduction is of interests due to the explosion of streaming data based applications and the requirement of adaptive statistical modeling, in many emerging fields, such as the modeling of energy end-use profile. Principal Component Analysis (PCA), is the classical way of dimensional redu…
A general study of symmetries in optimal control theory is given, starting from the presymplectic description of this kind of system. Then, Noether's theorem, as well as the corresponding reduction procedure (based on the application of the Marsden-Weinstein theorem adapted to the presymplectic case) are stated both in…
Paper identifies reductive MDPs, solving them in polynomial time.
A key question in Reinforcement Learning is which representation an agent can learn to efficiently reuse knowledge between different tasks. Recently the Successor Representation was shown to have empirical benefits for transferring knowledge between tasks with shared transition dynamics. This paper presents Model Featu…
New neural network method simplifies high-dimensional data.
FPG uses fractional calculus for efficient reinforcement learning with long-term memory.
Develops a new SPP algorithm with variance reduction for weakly convex optimization.
A new eigenvalue-based method speeds up Monte Carlo simulations.
Paper explores how risk-averse individuals' willingness to pay for insurance varies with risk probability.
We present local discriminative Gaussian (LDG) dimensionality reduction, a supervised dimensionality reduction technique for classification. The LDG objective function is an approximation to the leave-one-out training error of a local quadratic discriminant analysis classifier, and thus acts locally to each training po…
We show how to reduce the process of predicting general order statistics (and the median in particular) to solving classification. The accompanying theoretical statement shows that the regret of the classifier bounds the regret of the quantile regression under a quantile loss. We also test this reduction empirically ag…
Review and compare model order reduction methods for process engineering.
Reduces complexity of financial contagion dynamics on networks.
We present a method for fast resting-state fMRI spatial decomposi-tions of very large datasets, based on the reduction of the temporal dimension before applying dictionary learning on concatenated individual records from groups of subjects. Introducing a measure of correspondence between spatial decompositions of rest …
Reductive G-structures on a principal bundle Q are considered. It is shown that these structures, i.e. reductive G-subbundles P of Q, admit a canonical decomposition of the pull-back vector bundle over P. For classical G-structures, i.e. reductive G-subbundles of the linear frame bundle, suc…
VRER selectively reuses samples to improve policy optimization in complex systems.
New method learns low-dimensional models for systems with non-polynomial terms.
One of the key issues for imitation learning lies in making policy learned from limited samples to generalize well in the whole state-action space. This problem is much more severe in high-dimensional state environments, such as game playing with raw pixel inputs. Under this situation, even state-of-the-art adversary-b…
New method shows unitarity in quantization for toric manifolds.
In this paper we propose the macroblock scaling (MBS) algorithm, which can be applied to various CNN architectures to reduce their model size. MBS adaptively reduces each CNN macroblock depending on its information redundancy measured by our proposed effective flops. Empirical studies conducted with ImageNet and CIFAR-…
RMDA trains structured neural networks with regularization and variance reduction.
IKD uses eigen-decomposition for nonlinear dimensionality reduction.
Direct contextual policy search methods learn to improve policy parameters and simultaneously generalize these parameters to different context or task variables. However, learning from high-dimensional context variables, such as camera images, is still a prominent problem in many real-world tasks. A naive application o…
Harder's reduction theory provides filtrations of euclidean buildings that allow one to deduce cohomological and homological properties of S-arithmetic groups over global function fields. In this survey I will sketch the main points of Harder's reduction theory starting from Weil's geometry of numbers and the Riemann-R…
Efficiently simulates slow dynamics of high-dimensional stochastic systems.
Drago optimizes DRO problems with faster convergence.
Develops a new method for nonlinear dimension reduction using random features.
A method for robust reinforcement learning in large state spaces.
In this paper, we propose a Tensor Train Neighborhood Preserving Embedding (TTNPE) to embed multi-dimensional tensor data into low dimensional tensor subspace. Novel approaches to solve the optimization problem in TTNPE are proposed. For this embedding, we evaluate novel trade-off gain among classification, computation…
Unified model for reducing dimensions and clustering high-dimensional data.
Examines quantum mechanics equivalence with Newtonian geometry.
We show that on-policy policy gradient (PG) and its variance reduction variants can be derived by taking finite difference of function evaluations supplied by estimators from the importance sampling (IS) family for off-policy evaluation (OPE). Starting from the doubly robust (DR) estimator (Jiang & Li, 2016), we provid…
With some transformations, we convert the problem of option pricing under state-dependent volatility into an initial value problem of the Fokker-Planck equation with a certain potential. By using the Lie symmetry analysis and similarity reduction method, we are able to reduce the dimensions of the partial differential …
Evolution Strategies (ES) are a powerful class of blackbox optimization techniques that recently became a competitive alternative to state-of-the-art policy gradient (PG) algorithms for reinforcement learning (RL). We propose a new method for improving accuracy of the ES algorithms, that as opposed to recent approaches…
Framework corrects model form errors in structural dynamics predictions.
We present a modern formulation of Élie Cartan's structure theory for Lie pseudogroups and prove a reduction theorem that clarifies the role of Cartan's systatic system. The paper is divided into three parts. In part one, using notions coming from the theory of Lie groupoids and algebroids, we introduce the framework o…
Stochastic variance reduction algorithms have recently become popular for minimizing the average of a large, but finite number of loss functions. The present paper proposes a Riemannian stochastic quasi-Newton algorithm with variance reduction (R-SQN-VR). The key challenges of averaging, adding, and subtracting multipl…