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Forward-backward selection is one of the most basic and commonly-used feature selection algorithms available. It is also general and conceptually applicable to many different types of data. In this paper, we propose a heuristic that…
A curious property of randomized log-space search algorithms is that their outputs are often longer than their workspace. This leads to the question: how can we reproduce the results of a randomized log space computation without storing the…
This paper investigates the behavior of statistical ensembles under iteration map induced by discrete integrable Hamiltonian systems in deterministic case and stochastic case, addressing the problem from two perspectives: the Law of Large…
The goal of image oversegmentation is to divide an image into several pieces, each of which should ideally be part of an object. One of the simplest and yet most effective oversegmentation algorithms is known as local variation (LV)…
In the online learning with experts problem, an algorithm must make a prediction about an outcome on each of $T$ days (or times), given a set of $n$ experts who make predictions on each day (or time). The algorithm is given feedback on the…
Random projections are random linear maps, sampled from appropriate distributions, that approx- imately preserve certain geometrical invariants so that the approximation improves as the dimension of the space grows. The well-known…
This paper introduces a simple formalism for dealing with deterministic, non- deterministic and stochastic cellular automata in an unified and composable manner. This formalism allows for local probabilistic correlations, a feature which is…
We give a Markov chain based algorithm for sampling almost uniform solutions of constraint satisfaction problems (CSPs). Assuming a canonical setting for the Lov\'asz local lemma, where each constraint is violated by a small number of…
We apply recent ideas about complexity and randomness to the philosophy of laws and chances. We develop two ways to use algorithmic randomness to characterize probabilistic laws of nature. The first, a generative chance* law, employs a…
This thesis focuses on advancing probabilistic logic programming (PLP), which combines probability theory for uncertainty and logic programming for relations. The thesis aims to extend PLP to support both discrete and continuous random…
Stochastic optimization problems often involve data distributions that change in reaction to the decision variables. This is the case for example when members of the population respond to a deployed classifier by manipulating their features…
The algorithmic theory of randomness is well developed when the underlying space is the set of finite or infinite sequences and the underlying probability distribution is the uniform distribution or a computable distribution. These…
In this paper, we present perturbation analysis and randomized algorithms for the total least squares (TLS) problems. We derive the perturbation bound and check its sharpness by numerical experiments. Motivated by the recently popular…
The often elusive Poincar\'e recurrence can be witnessed in a completely separable system. For such systems, the problem of recurrence reduces to the classic mathematical problem of simultaneous Diophantine approximation of multiple…
Local algorithms on graphs are algorithms that run in parallel on the nodes of a graph to compute some global structural feature of the graph. Such algorithms use only local information available at nodes to determine local aspects of the…
By relaxing conditions for natural structure learning algorithms, a family of constraint-based algorithms containing all exact structure learning algorithms under the faithfulness assumption, we define localised natural structure learning…
Sequential change-point detection in non-Gaussian stochastic processes is challenging because the underlying densities are rarely known in real time. Classical parametric procedures such as CUSUM lose optimality under distributional…
Probabilistic Law Discovery (PLD) is a logic based Machine Learning method, which implements a variant of probabilistic rule learning. In several aspects, PLD is close to Decision Tree/Random Forest methods, but it differs significantly in…
We study the law of the iterated logarithm (LIL) for the maximum likelihood estimation of the parameters (as a convex optimization problem) in the generalized linear models with independent or weakly dependent ($\rho$-mixing, $m$-dependent)…
Stochastic approximation algorithm is a useful technique which has been exploited successfully in probability theory and statistics for a long time. The step sizes used in stochastic approximation are generally taken to be deterministic and…