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We propose to prune a random forest (RF) for resource-constrained prediction. We first construct a RF and then prune it to optimize expected feature cost & accuracy. We pose pruning RFs as a novel 0-1 integer program with linear constraints…

We propose a flexible yet interpretable model for high-dimensional data with time-varying second order statistics, motivated and applied to functional neuroimaging data. Motivated by the neuroscience literature, we factorize the covariances…

Dropout-based regularization methods can be regarded as injecting random noise with pre-defined magnitude to different parts of the neural network during training. It was recently shown that Bayesian dropout procedure not only improves…

In this paper, we propose a new scheme for the integration of the periodic nonlinear Schr\"{o}dinger equation and rigorously prove convergence rates at low regularity. The new integrator has decisive advantages over standard schemes at low…

Boson sampling is a fundamentally and practically important task that can be used to demonstrate quantum supremacy using noisy intermediate-scale quantum devices. In this work, we present classical sampling algorithms for single-photon and…

We propose a procedure to build a decision tree which approximates the performance of complex machine learning models. This single approximation tree can be used to interpret and simplify the predicting pattern of random forests (RFs) and…

Following arXiv:2303.02992, we develop an approach to the Hamiltonian theory of normal forms based on continuous averaging. We concentrate on the case of normal forms near an elliptic singular point, but unlike arXiv:2303.02992 we do not…

While data-driven model reduction techniques are well-established for linearizable mechanical systems, general approaches to reducing non-linearizable systems with multiple coexisting steady states have been unavailable. In this paper, we…

Regularization is essential for avoiding over-fitting to training data in network optimization, leading to better generalization of the trained networks. The label noise provides a strong implicit regularization by replacing the target…

This report will explore and answer fundamental questions about taking Fourier Transforms and tying it with recent advances in AI and neural architecture. One interpretation of the Fourier Transform is decomposing a signal into its…

The generation of curves and surfaces from given data is a well-known problem in Computer-Aided Design that can be approached using subdivision schemes. They are powerful tools that allow obtaining new data from the initial one by means of…

We examine normal form solutions of decision trees under typical choice functions induced by lower previsions. For large trees, finding such solutions is hard as very many strategies must be considered. In an earlier paper, we extended…

We extend the formalism whereby boson mappings can be derived from generalized coherent states to boson-fermion mappings for systems with an odd number of fermions. This is accomplished by constructing supercoherent states in terms of both…

A new renormalization scheme for theories with nontrivial internal symmetry is proposed. The scheme is regularization independent and respects the symmetry requirements.

Unsupervised representation learning methods are widely used for gaining insight into high-dimensional, unstructured, or structured data. In some cases, users may have prior topological knowledge about the data, such as a known cluster…

Dynamic trees are mixtures of tree structured belief networks. They solve some of the problems of fixed tree networks at the cost of making exact inference intractable. For this reason approximate methods such as sampling or mean field…

In this paper we revisit a Poincare lemma for foliated forms, with respect to a regular foliation, and compute the foliated cohomology for local models of integrable systems with singularities of nondegenerate type. A key point in this…

In many applications where collecting data is expensive, for example neuroscience or medical imaging, the sample size is typically small compared to the feature dimension. It is challenging in this setting to train expressive, non-linear…

Recently \cite{Horowitz:2022rpp,Horowitz:2022uak}, denominator regularisation (Den. Reg.) scheme has been proposed to handle divergences in quantum field theory. It is shown to yield results as simple as in dimensional regularisation scheme…

We present tree extraction in 3D images as a graph refinement task, of obtaining a subgraph from an over-complete input graph. To this end, we formulate an approximate Bayesian inference framework on undirected graphs using mean field…