相关论文: Approximate maximizers of intricacy functionals
In this paper, we introduce a method for approximating the solution to inference and optimization tasks in uncertain and deterministic reasoning. Such tasks are in general intractable for exact algorithms because of the large number of…
This paper investigates maximizers of the information divergence from an exponential family $E$. It is shown that the $rI$-projection of a maximizer $P$ to $E$ is a convex combination of $P$ and a probability measure $P_-$ with disjoint…
We introduce the concept of strong high-order approximate minimizers for nonconvex optimization problems. These apply in both standard smooth and composite non-smooth settings, and additionally allow convex or inexpensive constraints. An…
Recent work emphasizes that the maximum entropy principle provides a bridge between statistical mechanics models for collective behavior in neural networks and experiments on networks of real neurons. Most of this work has focused on…
Maximum entropy principle (MEP) offers an effective and unbiased approach to inferring unknown probability distributions when faced with incomplete information, while neural networks provide the flexibility to learn complex distributions…
In this work we discuss the problem of selecting suitable approximators from families of parameterized elementary functions that are known to be dense in a Hilbert space of functions. We consider and analyze published procedures, both…
We make the case for neural network objects and extend an already existing neural network calculus explained in detail in Chapter 2 on \cite{bigbook}. Our aim will be to show that, yes, indeed, it makes sense to talk about neural network…
We derive fundamental lower bounds on the connectivity and the memory requirements of deep neural networks guaranteeing uniform approximation rates for arbitrary function classes in $L^2(\mathbb R^d)$. In other words, we establish a…
We introduce the concepts of max-closedness and numeraires of convex subsets in the nonnegative orthant of the topological vector space of all random variables built over a probability space, equipped with a topology consistent with…
We propose an efficient algorithm for approximate computation of the profile maximum likelihood (PML), a variant of maximum likelihood maximizing the probability of observing a sufficient statistic rather than the empirical sample. The PML…
This is a preliminary article stating and proving a new maximum entropy theorem. The entropies that we consider can be used as measures of biodiversity. In that context, the question is: for a given collection of species, which frequency…
This article investigates emergence and complexity in complex systems that can share information on a network. To this end, we use a theoretical approach from information theory, computability theory, and complex networks. One key studied…
We show the existence of a deep neural network capable of approximating a wide class of high-dimensional approximations. The construction of the proposed neural network is based on a quasi-optimal polynomial approximation. We show that this…
We propose a general method for optimization with semi-infinite constraints that involve a linear combination of functions, focusing on the case of the exponential function. Each function is lower and upper bounded on sub-intervals by…
We study the computational complexity of approximating general constrained Markov decision processes. Our primary contribution is the design of a polynomial time $(0,\epsilon)$-additive bicriteria approximation algorithm for finding optimal…
As is the case for many curved exponential families, the computation of maximum likelihood estimates in a multivariate normal model with a Kronecker covariance structure is typically carried out with an iterative algorithm, specifically, a…
We study the optimization version of constraint satisfaction problems (Max-CSPs) in the framework of parameterized complexity; the goal is to compute the maximum fraction of constraints that can be satisfied simultaneously. In standard…
Network control refers to a very large and diverse set of problems including controllability of linear time-invariant dynamical systems, where the objective is to select an appropriate input to steer the network to a desired state. There…
We study the approximation capabilities of two families of univariate polynomials that arise in applications of quantum signal processing. Although approximation only in the domain $[0,1]$ is physically desired, these polynomial families…
The volume of phase space may grow super-exponentially ("explosively") with the number of degrees of freedom for certain types of complex systems such as those encountered in biology and neuroscience, where components interact and create…