Related papers: On the Approximation Complexity of Matrix Product …
When a matrix A with n columns is known to be well approximated by a linear combination of basis matrices B_1,..., B_p, we can apply A to a random vector and solve a linear system to recover this linear combination. The same technique can…
Sharp bounds on partially identified parameters are often given by the values of linear programs (LPs). This paper introduces a novel estimator of the LP value. Unlike existing procedures, our estimator is root-n-consistent, pointwise in…
Restricted Boltzmann Machine (RBM) is an importan- t generative model modeling vectorial data. While applying an RBM in practice to images, the data have to be vec- torized. This results in high-dimensional data and valu- able spatial…
We study practical approximations to Kolmogorov prefix complexity (K) using IMP2, a high-level programming language. Our focus is on investigating the interpreter optimality for this language as the reference machine for the Coding Theorem…
Backpropagation of error (backprop) is a powerful algorithm for training machine learning architectures through end-to-end differentiation. However, backprop is often criticised for lacking biological plausibility. Recently, it has been…
The restricted Boltzmann machine (RBM) is a flexible tool for modeling complex data, however there have been significant computational difficulties in using RBMs to model high-dimensional multinomial observations. In natural language…
We study computational and statistical aspects of learning Latent Markov Decision Processes (LMDPs). In this model, the learner interacts with an MDP drawn at the beginning of each epoch from an unknown mixture of MDPs. To sidestep known…
Extracting automatically the complex set of features composing real high-dimensional data is crucial for achieving high performance in machine--learning tasks. Restricted Boltzmann Machines (RBM) are empirically known to be efficient for…
Stoquastic Hamiltonians are characterized by the property that their off-diagonal matrix elements in the standard product basis are real and non-positive. Many interesting quantum models fall into this class including the Transverse field…
We discuss the relations between restricted Boltzmann machine (RBM) states and the matrix product states (MPS) for the ground states of 1D translational invariant stabilizer codes. A generic translational invariant and finitely connected…
Bayesian optimization (BO) for high-dimensional constrained problems remains a significant challenge due to the curse of dimensionality. We propose Local Constrained Bayesian Optimization (LCBO), a novel framework tailored for such…
Generalized Method of Moments (GMM) estimators in their various forms, including the popular Maximum Likelihood (ML) estimator, are frequently applied for the evaluation of complex econometric models with not analytically computable moment…
Bobkov (J. Theoret. Probab. 18(2) (2005) 399-412) investigated an approximate de Finetti representation for probability measures, on product measurable spaces, which are symmetric under permutations of coordinates. One of the main results…
The rough Heston model is a very popular recent model in mathematical finance; however, the lack of Markov and semimartingale properties poses significant challenges in both theory and practice. A way to resolve this problem is to use…
We study the problem of finding a (pure) product state with optimal fidelity to an unknown $n$-qubit quantum state $\rho$, given copies of $\rho$. This is a basic instance of a fundamental question in quantum learning: is it possible to…
In recent years, researchers have made significant progress in devising reinforcement-learning algorithms for optimizing linear temporal logic (LTL) objectives and LTL-like objectives. Despite these advancements, there are fundamental…
We present several improvements of the infinite matrix product state (iMPS) algorithm for finding ground states of one-dimensional quantum systems with long-range interactions. As a main new ingredient we introduce the superposed…
A matrix optimization problem over an uncertain linear system on finite horizon (abbreviated as MOPUL) is studied, in which the uncertain transition matrix is regarded as a decision variable. This problem is in general NP-hard. By using the…
In this paper, we take an in-depth look at the complexity of a hitherto unexplored Multiobjective Spanner (MSp) problem. The MSp is a multiobjective generalization of the well-studied Minimum t-Spanner problem. This multiobjective approach…
A key goal in the design of probabilistic inference algorithms is identifying and exploiting properties of the distribution that make inference tractable. Lifted inference algorithms identify symmetry as a property that enables efficient…