Pre-conditioning is a well-known concept that can significantly improve the convergence of optimization algorithms. For noise-free problems, where good pre-conditioners are not known a priori, iterative linear algebra methods offer one way to efficiently construct them. For the stochastic optimization problems that dom…
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48 results for “conditionally linear”
Develops CLDS models to model neural activity with nonlinear dynamics.
problem Complex, nonlinear dynamics in neural population activity.
method Conditionally Linear Dynamical System (CLDS) models using Gaussian Process (GP) priors.
result CLDS models can perform well even in data-limited conditions.
A one-factor asset pricing model with an Ornstein--Uhlenbeck process as its state variable is studied under partial information: the mean-reverting level and the mean-reverting speed parameters are modeled as hidden/unobservable stochastic variables. No-arbitrage pricing formulas for derivative securities written on a …
Transformers can solve complex filtering problems for non-Gaussian signals.
problem Non-linear and non-Markovian filtering problems for conditionally Gaussian signals.
method Continuous-time transformer models called filterformers.
result Filterformers can approximate the conditional law of non-Markovian and conditionally Gaussian signal processes.
Risk bounds for Classification and Regression Trees (CART, Breiman et. al. 1984) classifiers are obtained under a margin condition in the binary supervised classification framework. These risk bounds are obtained conditionally on the construction of the maximal deep binary tree and permit to prove that the linear penal…
We describe a mechanism by which artificial neural networks can learn rapid adaptation - the ability to adapt on the fly, with little data, to new tasks - that we call conditionally shifted neurons. We apply this mechanism in the framework of metalearning, where the aim is to replicate some of the flexibility of human …
Study improves conformal prediction for missing covariate data.
problem Uncertainty quantification with missing covariate values.
method Generalized conformalized quantile regression framework, missing data augmentation.
result Improved prediction intervals valid conditionally to missing data patterns.
Jump Markov linear models consists of a finite number of linear state space models and a discrete variable encoding the jumps (or switches) between the different linear models. Identifying jump Markov linear models makes for a challenging problem lacking an analytical solution. We derive a new expectation maximization …
We study how convergence of an observer whose state lives in a copy of the given system's space can be established using a Riemannian metric. We show that the existence of an observer guaranteeing the property that a Riemannian distance between system and observer solutions is nonincreasing implies that the Lie derivat…
Algorithm estimates parameters over time-varying graphs without special assumptions.
problem Estimating parameters over time-varying graphs without assuming independence.
method Decentralized online regularized learning with innovation, consensus, and regularization terms.
result Estimations converge almost surely under certain conditions.
We consider the problem of maximizing expected utility from terminal wealth in models with stochastic factors. Using martingale methods and a conditioning argument, we determine the optimal strategy for power utility under the assumption that the increments of the asset price are independent conditionally on the factor…
Prominent Roles of Conditionally Invariant Components in Domain Adaptation: Theory and Algorithmsstat.ML
New algorithm uses conditionally invariant components to improve domain adaptation performance.
problem Improving domain adaptation performance when source and target data distributions differ.
method Conditionally invariant components (CICs) and importance-weighted conditional invariant penalty (IW-CIP) algorithm.
result New algorithm provides target risk guarantees and addresses label-flipping features.
This work explores adaptive strategies for multi-armed bandits with causal structure, achieving optimal regret bounds.
problem Adapting to causal structure in multi-armed bandits with additional observed variables.
method Reduction to linear bandits and establishment of Pareto optimal frontier of adaptive rates.
result Established upper and lower bounds on adaptive rates, resolving open questions.
CW-Gen models improve probabilistic time series forecasting by incorporating prior information.
problem Challenges in probabilistic forecasting of multivariate time series due to non-stationarity, inter-variable dependencies, and distribution shifts.
method CW-Gen framework that incorporates prior information through conditional whitening. JMCE learns conditional mean and covariance, improving sample quality.
result CW-Gen consistently enhances predictive performance, capturing non-stationary dynamics and inter-variable correlations more effectively than prior-free approaches.
Many complex dynamical phenomena can be effectively modeled by a system that switches among a set of conditionally linear dynamical modes. We consider two such models: the switching linear dynamical system (SLDS) and the switching vector autoregressive (VAR) process. Our Bayesian nonparametric approach utilizes a hiera…
Unified strategy for efficient data compression and model estimation.
problem Limited interactive exploration and data interaction in linear model development and deployment.
method Conditionally sufficient statistics for optimal data compression and estimation of linear models.
result Linear models can be estimated from compressed data without loss of parameters or covariances.
Unified bounds for iterative algorithms with Gaussian data matrices.
problem Establishing non-asymptotic bounds for iterative algorithms with Gaussian data.
method Explicit coupling between iterates and Gaussian process with deterministic covariance.
result Tight, dimension-free bounds for generalized first-order methods.
Introduces CSLC models to bridge deep generative models and classical algorithms.
problem Mode collapse and memorization issues in deep generative models and restrictive assumptions in classical algorithms.
method Introduces conditionally strongly log-concave (CSLC) models, factorizing data distribution into strongly log-concave conditional distributions.
result Efficient parameter estimation and sampling algorithms with theoretical guarantees for non-log-concave data distributions.
Providing meaningful privacy to users of location based services is particularly challenging when multiple locations are revealed in a short period of time. This is primarily due to the tremendous degree of dependence that can be anticipated between points. We propose a Rényi differentially private framework for boundi…
This paper addresses missing covariates in stochastic linear bandits, providing a high-probability regret bound.
problem Effect of missing covariates on regret in stochastic linear bandit algorithms.
method Proposes an algorithm that provides a high-probability upper bound on regret in terms of covariate sampling probabilities.
result Regret degrades due to missingness by at most , where is the minimum probability of observing covariates.
Modeling financial returns as conditionally independent random variables explains power-law tails.
problem Understanding the distribution of financial returns and their relation to volatility.
method Assuming returns are conditionally independent given volatility, which varies randomly over time.
result Returns distribution can be described by the sum of conditionally independent random variables, showing scaling and power-law tails.
The paper proves the law of one price in a continuous-time setting without friction.
problem Identifying conditions under which the law of one price holds in a continuous-time setting without frictions.
method Formulating a new mechanism for LOP failure and proving a novel variant of the uniform boundedness principle.
result Establishes the equivalence of the economic concept of LOP with the probabilistic property of the existence of a local $\scr{E}$-martingale state price density.
The paper examines properties of GW optimal transport plans, showing they can be sparse and permutation-supported.
problem Properties of Gromov-Wasserstein optimal transport plans.
method Exploration of sparsity, permutation support, and cyclical monotonicity properties.
result GW optimal plans can be sparse and permutation-supported under certain conditions.
Optimizes mixture models without parametrizing distributions using tensor decomposition.
problem Estimating conditionally-independent mixture models in high dimensions.
method Alternating least squares optimization scheme for tensor decomposition.
result Competitive performance and applicability to various models and applications.
Proposes iVDFM for identifying latent factors in multivariate time series.
problem Identifying latent factors in multivariate time series with structural dynamics.
method Identifiable Variational Dynamic Factor Model (iVDFM) with iVAE-style conditioning.
result Identifiable latent factors up to permutation and component-wise affine transformations.
Adaptive source selection for positive transfer in linear models improves target dataset performance.
problem Limited task-specific labeled data in business settings.
method Greedily decides from which sources and how many samples to incorporate into the target dataset using an accept/reject rule based on a data-dependent estimate of the transfer gain.
result Consistent gains over classical and recent strong baselines while avoiding negative transfer.
CIRCE measures conditional independence for learning invariant features.
problem Learning invariant features while being conditionally independent of a distractor.
method CIRCE is a measure of conditional independence applied as a regularizer in feature learning.
result CIRCE provides a zero value if and only if features are conditionally independent of the distractor given the target.
New model captures time and mark inter-dependence in TPPs.
problem Limited predictive performance of conditionally independent TPP models on entangled time and mark interactions.
method Developed a multivariate TPP that models conditional inter-dependence of time and mark, using both intensity-based and intensity-free models.
result Proposed TPP models outperform conditionally independent and dependent models in standard prediction tasks.
Long Memory and Volatility Clustering: is the empirical evidence consistent across stock markets?q-fin.ST
Long memory and volatility clustering are two stylized facts frequently related to financial markets. Traditionally, these phenomena have been studied based on conditionally heteroscedastic models like ARCH, GARCH, IGARCH and FIGARCH, inter alia. One advantage of these models is their ability to capture nonlinear dynam…
This paper explores adaptive methods in over-parameterized linear regression.
problem Understanding why neural networks generalize well in over-parameterized settings.
method Characterizes two sub-classes of adaptive methods and their generalization performance.
result Adaptive methods in over-parameterized linear regression converge to the minimum norm solution.
We revisit the Bayesian online inference problems for the linear dynamic systems (LDS) under non- Gaussian environment. The noises can naturally be non-Gaussian (skewed and/or heavy tailed) or to accommodate spurious observations, noises can be modeled as heavy tailed. However, at the cost of such noise robustness, the…
We characterize the combinatorial structure of conditionally-i.i.d. sequences of negative binomial processes with a common beta process base measure. In Bayesian nonparametric applications, such processes have served as models for latent multisets of features underlying data. Analogously, random subsets arise from cond…
An inductive probabilistic classification rule must generally obey the principles of Bayesian predictive inference, such that all observed and unobserved stochastic quantities are jointly modeled and the parameter uncertainty is fully acknowledged through the posterior predictive distribution. Several such rules have b…
Linear-cost unbiased estimates for complex models via couplings.
problem High-dimensional Bayesian models with crossed effects and matrix factorization.
method Coupled Gibbs samplers for linear computational cost.
result Unbiased posterior estimates at linear cost.
Automated denoising score matching handles nonlinear diffusion processes.
problem Nonlinear diffusion processes limit generative modeling and property estimation.
method Local-DSM using local increments and Taylor expansions.
result Tractable training and score estimation for nonlinear diffusion processes.
New research challenges the independence assumption in neurosymbolic learning, leading to overconfident predictions and unrepresentable uncertainty.
problem The independence assumption in neurosymbolic learning systems can lead to overconfident predictions and hinder uncertainty quantification.
method The study proves the limitations of the independence assumption and introduces new loss functions that are non-convex and difficult to optimise.
result Neurosymbolic learning systems using the independence assumption are prone to overconfidence and cannot represent uncertainty over multiple valid options.
New method models stopping times that can be equal with non-zero probability.
problem Standard stopping time models assume conditional independence, limiting flexibility.
method Modified Cox construction with bivariate exponential distribution.
result Created a family of stopping times that can be equal with positive probability.
New PFPPs based on rank-dependent utility for better performance control.
problem Improving performance prediction in systems with short-term control.
method Introduces rank-dependent PFPPs, solves integral equations via Volterra theory.
result Existence of rank-dependent PFPPs under specific market conditions.
We develop constructions for exchangeable sequences of point processes that are rendered conditionally-i.i.d. negative binomial processes by a (possibly unknown) random measure called the base measure. Negative binomial processes are useful in Bayesian nonparametrics as models for random multisets, and in applications …
Compressed Gaussian Processstat.ML
Nonparametric regression for massive numbers of samples (n) and features (p) is an increasingly important problem. In big n settings, a common strategy is to partition the feature space, and then separately apply simple models to each partition set. We propose an alternative approach, which avoids such partitioning and…
We derive fundamental sample complexity bounds for recovering sparse and structured signals for linear and nonlinear observation models including sparse regression, group testing, multivariate regression and problems with missing features. In general, sparse signal processing problems can be characterized in terms of t…
The study uses Bayesian Hidden Markov Models to predict cryptocurrency returns.
problem Predicting the volatility and trends of cryptocurrencies.
method Bayesian Hidden Markov Models with four states to capture different return characteristics.
result The NHHM model with four states outperforms other models in predicting cryptocurrency returns.
AlphaGrad optimizes memory usage in RL algorithms by normalizing gradients.
problem Memory overhead and hyperparameter complexity in adaptive optimizers.
method Tensor-wise L2 normalization followed by a smooth hyperbolic tangent transformation controlled by a single parameter.
result AlphaGrad provides enhanced training stability and competitive performance in various RL algorithms.
The multiresolution Gaussian process (GP) has gained increasing attention as a viable approach towards improving the quality of approximations in GPs that scale well to large-scale data. Most of the current constructions assume full independence across resolutions. This assumption simplifies the inference, but it under…
We investigate the effects of the unsupervised pre-training method under the perspective of information theory. If the input distribution displays multiple views of the supervision, then unsupervised pre-training allows to learn hierarchical representation which communicates these views across layers, while disentangli…
Auto-regressive conditionally heteroskedastic (ARCH) family models are still used, by practitioners in business and economic policy making, as a conditional volatility forecasting models. Furthermore ARCH models still are attracting an interest of the researchers. In this contribution we consider the well known GARCH(1…
We investigate Fano schemes of conditionally generic intersections, i.e. of hypersurfaces in projective space chosen generically up to additional conditions. Via a correspondence between generic properties of algebraic varieties and events in probability spaces that occur with probability one, we use the obtained resul…
We consider multi-task regression models where observations are assumed to be a linear combination of several latent node and weight functions, all drawn from Gaussian process (GP) priors that allow nonzero covariance between grouped latent functions. We show that when these grouped functions are conditionally independ…