23,547 research outputs found
A Method of Moments for Mixture Models and Hidden Markov Models
Mixture models are a fundamental tool in applied statistics and machine
learning for treating data taken from multiple subpopulations. The current
practice for estimating the parameters of such models relies on local search
heuristics (e.g., the EM algorithm) which are prone to failure, and existing
consistent methods are unfavorable due to their high computational and sample
complexity which typically scale exponentially with the number of mixture
components. This work develops an efficient method of moments approach to
parameter estimation for a broad class of high-dimensional mixture models with
many components, including multi-view mixtures of Gaussians (such as mixtures
of axis-aligned Gaussians) and hidden Markov models. The new method leads to
rigorous unsupervised learning results for mixture models that were not
achieved by previous works; and, because of its simplicity, it offers a viable
alternative to EM for practical deployment
Accelerating Cooperative Planning for Automated Vehicles with Learned Heuristics and Monte Carlo Tree Search
Efficient driving in urban traffic scenarios requires foresight. The
observation of other traffic participants and the inference of their possible
next actions depending on the own action is considered cooperative prediction
and planning. Humans are well equipped with the capability to predict the
actions of multiple interacting traffic participants and plan accordingly,
without the need to directly communicate with others. Prior work has shown that
it is possible to achieve effective cooperative planning without the need for
explicit communication. However, the search space for cooperative plans is so
large that most of the computational budget is spent on exploring the search
space in unpromising regions that are far away from the solution. To accelerate
the planning process, we combined learned heuristics with a cooperative
planning method to guide the search towards regions with promising actions,
yielding better solutions at lower computational costs
Mixed-Integer Convex Nonlinear Optimization with Gradient-Boosted Trees Embedded
Decision trees usefully represent sparse, high dimensional and noisy data.
Having learned a function from this data, we may want to thereafter integrate
the function into a larger decision-making problem, e.g., for picking the best
chemical process catalyst. We study a large-scale, industrially-relevant
mixed-integer nonlinear nonconvex optimization problem involving both
gradient-boosted trees and penalty functions mitigating risk. This
mixed-integer optimization problem with convex penalty terms broadly applies to
optimizing pre-trained regression tree models. Decision makers may wish to
optimize discrete models to repurpose legacy predictive models, or they may
wish to optimize a discrete model that particularly well-represents a data set.
We develop several heuristic methods to find feasible solutions, and an exact,
branch-and-bound algorithm leveraging structural properties of the
gradient-boosted trees and penalty functions. We computationally test our
methods on concrete mixture design instance and a chemical catalysis industrial
instance
Learning to Segment and Represent Motion Primitives from Driving Data for Motion Planning Applications
Developing an intelligent vehicle which can perform human-like actions
requires the ability to learn basic driving skills from a large amount of
naturalistic driving data. The algorithms will become efficient if we could
decompose the complex driving tasks into motion primitives which represent the
elementary compositions of driving skills. Therefore, the purpose of this paper
is to segment unlabeled trajectory data into a library of motion primitives. By
applying a probabilistic inference based on an iterative
Expectation-Maximization algorithm, our method segments the collected
trajectories while learning a set of motion primitives represented by the
dynamic movement primitives. The proposed method utilizes the mutual
dependencies between the segmentation and representation of motion primitives
and the driving-specific based initial segmentation. By utilizing this mutual
dependency and the initial condition, this paper presents how we can enhance
the performance of both the segmentation and the motion primitive library
establishment. We also evaluate the applicability of the primitive
representation method to imitation learning and motion planning algorithms. The
model is trained and validated by using the driving data collected from the
Beijing Institute of Technology intelligent vehicle platform. The results show
that the proposed approach can find the proper segmentation and establish the
motion primitive library simultaneously
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