Paper shows pricing rules affect insider's optimal strategy in Kyle-Back models.
problem Effect of pricing rules on insider's optimal strategy in Kyle-Back models.
method Analyzed a large class of pricing rules and derived necessary conditions for consistency with equilibrium.
result Pricing rules can lead to infinite value function for insiders when strategies are restricted, contradicting folk result.
Study on Kähler metrics on ruled surfaces, proving existence and non-existence.
problem Existence and non-existence of Kähler metrics on minimal ruled surfaces.
method Analysis of twisted and coupled constant scalar curvature Kähler metrics.
result Bound for Chen-Cheng invariant on ruled surfaces.
NeuRules learns interpretable rule lists from data without pre-discretization.
problem Interpretable rule lists for high-stakes decisions in machine learning.
method Neuro-symbolic continuous optimization with temperature annealing.
result NeuRules outperforms existing methods in learning interpretable rule lists.
Players choose rebalancing rules to maximize their wealth relative to others in a continuous-time trading game.
problem Optimizing wealth in a continuous-time trading game between two players.
method Players choose rebalancing rules to maximize their expected wealth ratio, using the Kelly rule in equilibrium.
result The Kelly rule emerges as the optimal strategy in both short and long time intervals.
RIPE predicts and explains continuous/discrete data with sparse rule sets.
problem Predicting and explaining continuous/discrete data.
method RIPE infers a model from a sample, extracting a sparse set of hyperrectangles (rules) to partition the feature space.
result RIPE efficiently predicts and explains data, superior to other algorithms.
The nearest neighbor rule is proven consistent in a broad setting.
problem Proving consistency of the nearest neighbor rule in various settings.
method Proving online consistency for all measurable functions in doubling metric spaces under mild assumptions.
result The nearest neighbor rule is online consistent in all measurable functions in doubling metric spaces.
TransINT embeds KGs by preserving implication rules, outperforming existing methods.
problem Embedding KGs while preserving relation implications for better access and analysis.
method Isomorphic intersections of linear subspaces with shared parameters for missing facts.
result Significant performance improvement in link prediction and triple classification.
SupRB learns rules for continuous decision problems from examples.
problem Learning from continuous choices and explaining decisions to operators.
method SupRB is a supervised rule-based learning system for multi-dimensional continuous problems.
result SupRB provides human-understandable rules for optimal choices and quality predictions.
Proposes a new decision rule for continuous treatments.
problem Developing personalized treatment recommendations for continuous treatments.
method Jump interval-learning method to estimate conditional mean of outcomes.
result Optimal interval-valued decision rule (I2DR) for continuous treatments.
Develops deep jump learning for continuous treatment OPE.
problem Estimating mean outcomes under new treatment rules using historical data from different rules.
method Adaptive deep discretization of continuous treatment space using deep learning and multi-scale change point detection.
result Validated method through theoretical results, simulations, and real application to Warfarin Dosing.
Improves observation-driven filters using proper scoring rules for better parameter estimation.
problem Improves parameter estimation in observation-driven filters.
method Replaces likelihood score with negative parameter derivative of a proper scoring rule.
result Establishes consistency and asymptotic normality for estimation.
New STDP rule for spiking neurons solves discrete action reinforcement learning tasks.
problem Applying standard STDP to discrete action reinforcement learning tasks.
method Feedback-modulated TD-STDP learning rule for spiking neuron networks.
result Feedback modulation improves credit assignment in reinforcement learning.
Kernel method optimizes personalized dose rules for patients.
problem Finding optimal individualized dose rules for patients.
method Kernel assisted learning method for estimating optimal dose rules.
result The method identifies the optimal individualized dose rule and produces favorable outcomes.
Paper solves a trading game for stocks that jump and diffuse, finding the Kelly rule is optimal.
problem Trading game for stocks that can jump and diffuse.
method Solves a zero-sum game with a payoff kernel, finding the Kelly rule for jump diffusions.
result The Kelly rule is the optimal strategy for outperforming traders in a trading game.
Wittgenstein's Rule Following evolves datasets by extrapolating structural descriptors.
problem Generating meaningful continuations of evolving datasets.
method Wittgenstein's Rule Following (WRF) uses structural descriptors to extrapolate trajectories and average historical descriptors.
result WRF can generate meaningful continuations of evolving datasets.
New scoring rules for multivariate distributions and level sets.
problem Evaluating forecast accuracy for multivariate distributions and level sets.
method Theoretical framework for scoring rules, decomposition of multivariate scoring functions, numerical algorithm for computation.
result New scoring functions for multivariate distributions and level sets, including density and cumulative distribution level sets.
This paper discusses issues in mining user behavioral rules for context-aware mobile apps.
problem Mining contextual behavioral rules from smartphone data.
method Addressing quality of data, relevancy of contexts, discretization, rule discovery, semantic understanding, and dynamic rule updating.
result Potential solutions for mining user behavioral rules for context-aware mobile apps.
New framework optimizes decisions under uncertainty considering causal and continuous data.
problem Optimizing decisions under uncertain distributions with causal and continuous data structures.
method Developed a framework using Causal Sinkhorn DRO with Soft Regression Forest decision rules.
result Framework provides interpretable and tractable decision rules for optimizing under uncertainty.
Paper explores subdifferential chain rules for matrix factorization and related machine learning models.
problem Clarke subdifferential chain rules for matrix factorization and factorization machines.
method Analyzes conditions for subdifferential chain rules to hold, especially for overparameterized models.
result Subdifferential chain rules hold for matrix factorization and factorization machines under certain conditions.
This paper formulates a model of utility for a continuous time framework that captures the decision-maker's concern with ambiguity about both volatility and drift. Corresponding extensions of some basic results in asset pricing theory are presented. First, we derive arbitrage-free pricing rules based on hedging argumen…
Paper optimizes combining expert predictions using CRPS loss.
problem Optimizing combining expert predictions in online learning.
method Combines probabilistic forecasts using CRPS loss function in the prediction with expert advice framework.
result Time-independent upper bound for the regret of the Vovk's aggregating algorithm using CRPS as a loss function is obtained.
In this work, we consider the hedging error due to discrete trading in models with jumps. Extending an approach developed by Fukasawa [In Stochastic Analysis with Financial Applications (2011) 331-346 Birkhäuser/Springer Basel AG] for continuous processes, we propose a framework enabling us to (asymptotically) optimize…
Study optimizes financial investments in large markets.
problem Maximizing expected utility in large financial markets with factor structures.
method Establishes optimizers under weaker assumptions, studies convergence of optimal investments.
result Continuity rules hold for optimal investments in small and large markets.
Framework learns portable representations for diverse tasks.
problem Creating task-independent abstract representations for diverse environments.
method Autonomously learns portable representations in egocentric space.
result Portable representations enable task-independent planning and transfer.
Develops a chain rule for ReLU networks and extends approximation theory to global error estimates.
problem Applying standard chain rule to ReLU networks and extending approximation results globally.
method Introduces a derivative for ReLU networks and converts bounded domain results to global estimates.
result Extends neural network approximation theory to include regularity properties for ReLU networks.
Study evaluates multivariate forecasting scoring rules and proposes new copula-based ones.
problem Evaluating and improving multivariate probabilistic forecasting methods.
method Analysis and comparison of existing scoring rules, development of copula-based scoring rules, simulation studies, and real data analysis.
result Proposed copula-based scoring rules provide strong distinction between models with correct and incorrect dependency structures.
This paper extends the classical consumption and portfolio rules model in continuous time (Merton 1969, 1971) to the framework of decision-makers with time-inconsistent preferences. The model is solved for different utility functions for both, naive and sophisticated agents, and the results are compared. In order to so…
Simple rules ensure gradient descent adapts to local geometry, converging for convex and nonconvex problems.
problem Minimizing convex and nonconvex functions efficiently.
method Two rules: don't increase stepsize too fast and don't overstep local curvature.
result Method converges for convex and nonconvex problems, even with infinite global smoothness.
Efficient algorithm for global optimization of multivariate Lipschitz functions.
problem Global optimization of multivariate Lipschitz continuous functions.
method Proposes an efficient minimax optimal algorithm using a predetermined query creation rule.
result Achieves an average regret bound of O ( L n T − 1 n ) O(L\sqrt{n}T^{-\frac{1}{n}}) O ( L n T − n 1 ) , minimax optimal. RSI uses Bayesian inference to monitor compliance in rule-governed domains.
problem Structural obstacles in compliance monitoring, including unlabeled outcomes and selective withholding of evidence.
method Rule-State Inference (RSI) treats formalized rules as Bayesian priors and infers compliance states through mean-field variational inference.
result RSI delivers formal guarantees of adaptability, consistency, and convergence, validated on a synthetic enterprise benchmark.
New methods for Bayesian inference using mean shift particle systems.
problem Approximating expectations with unnormalized densities in Bayesian inference.
method Mean shift interacting particle systems that minimize maximum mean discrepancy (MMD).
result Mean shift interacting particle systems converge quickly and capture complex distributions.
We learn sensor trees from training data to minimize sensor acquisition costs during test time. Our system adaptively selects sensors at each stage if necessary to make a confident classification. We pose the problem as empirical risk minimization over the choice of trees and node decision rules. We decompose the probl…
Using a model of wealth distribution where traders are characterized by quenched random saving propensities and trade among themselves by bipartite transactions, we mimic the enhanced rates of trading of the rich by introducing the preferential selection rule using a pair of continuously tunable parameters. The biparti…
Open problem: Establishing bounds for Cayley-table completion to discover discrete algorithmic axioms.
problem Discovering discrete algorithmic axioms missing in deep learning.
method Cayley-table completion as a testbed for algorithmic complexity minimization.
result Formal exact recovery bounds for Cayley-table completion.
Bayesian learning rule trains binary neural networks effectively.
problem Training binary neural networks is challenging due to discrete optimization.
method Proposes the Bayesian learning rule to estimate Bernoulli weights.
result Obtains state-of-the-art performance and enables uncertainty estimation.
We introduce a simple stochastic volatility model, whose novelty consists in taking into account hitting times of the asset price, and study the optimal stopping problem corresponding to a put option whose time horizon (after the asset price hits a certain level) is exponentially distributed. We obtain explicit optimal…
Signature kernel scoring rule improves weather forecasting by capturing temporal and spatial dependencies.
problem Lack of suitable scoring rules for probabilistic weather forecasting.
method Reframe weather variables as continuous paths using iterated integrals (signature kernels) to capture temporal and spatial dependencies.
result Signature kernel scoring rule outperforms conventional methods in weather forecasting, especially for long-term forecasts.
Derives effective continuous dynamics for adaptive SGD methods.
problem Analyzing noise in adaptive SGD methods.
method Stochastic modified equations framework and Malladi's scaling rules.
result Sampling-induced noise in SGD limits to independent Brownian motions.
A method is given for calculating the strict minimum message length (SMML) estimator for 1-dimensional exponential families with continuous sufficient statistics. A set of n n n equations are found that the n n n cut-points of the SMML estimator must satisfy. These equations can be solved using Newton's method and this app…
The problem of pricing Bermudan options using Monte Carlo and a nonparametric regression is considered. We derive optimal non-asymptotic bounds for a lower biased estimate based on the suboptimal stopping rule constructed using some estimates of continuation values. These estimates may be of different nature, they may …
Study compares different scoring rules for machine-learned weather forecasts, finding scale-awareness improves forecast realism.
problem Improving the accuracy of machine-learned probabilistic weather forecasts.
method Comparison of scoring rules (CRPS, fair global energy score, graph energy score) and analysis of their impact on forecast field spectra.
result Scale-awareness improves forecast realism, particularly in the tropics.
Kyle (1985) builds a pioneering and influential model, in which an insider with long-lived private information submits an optimal order in each period given the market maker's pricing rule. An inconsistency exists to some extent in the sense that the ``constant pricing rule " actually assumes an adaptive expected price…
New algorithm optimizes Hölder continuous functions efficiently.
problem Optimizing Hölder continuous multivariate functions.
method Uses a query creation rule for global optimization, avoiding proxy functions.
result Achieves an average regret bound of $O(T^{- racα{n}})$ for Hölder exponent α α α . New model CRS combines transparency and high performance for classification.
problem Need models with transparent structure and high classification performance.
method Concept Rule Sets (CRS) with Multilayer Logical Perceptron (MLLP) and Random Binarization (RB).
result CRS outperforms state-of-the-art approaches and has low complexity.
Study logical generalization in GNNs using a new benchmark.
problem Understanding how GNNs adapt to new logical tasks.
method Developed GraphLog benchmark suite for logical tasks, evaluated GNNs in supervised, pretraining, and continual learning settings.
result Logical diversity during training affects GNNs' ability to generalize.
Quantum models use complex Hilbert spaces for uncertainty.
problem Modeling dynamics in continuous-valued features.
method Quantum Graphical Models (QGMs) and Hilbert Space Embedding (HSE).
result HSE-HQMMs are competitive with state-of-the-art models.
Optimal task order improves continual learning performance.
problem Challenges in neural networks learning multiple tasks in sequence.
method Linear teacher-student model with latent factors, derived analytical expression.
result Two principles for optimal task order: least representative first and dissimilar adjacent tasks.
Paper introduces FDM for efficient training of Neural SDEs.
problem Training Neural SDEs using existing methods is computationally expensive and unstable.
method Developed a novel scoring rule called Finite Dimensional Matching (FDM) to bypass signature kernels and reduce training complexity.
result FDM achieves superior performance in terms of computational efficiency and generative quality.