Convex Optimization

Compressive wideband spectrum sensing for fixed frequency spectrum allocation

by Yipeng Liu

A Robust Beamformer Based on Weighted Sparse Constraint

by Yipeng Liu

Robust Compressive Wideband Spectrum Sensing with Sampling Distortion

by Yipeng Liu

Sparse Support Recovery with Phase-Only Measurements

by Yipeng Liu

Total Variation Minimization Based Compressive Wideband Spectrum Sensing for Cognitive Radios

by Yipeng Liu

Optimization Algorithms in the Reconstruction of MR Images: A Comparative Study

by Mateusz Malinowski

Time that an imaging device needs to produce results is one of the most crucial factors in
medical imaging.... more Time that an imaging device needs to produce results is one of the most crucial factors in
medical imaging. Shorter scanning duration causes fewer artifacts such as those created by
the patient motion. In addition, it increases patient comfort and in the case of some imaging
modalities also decreases exposure to radiation.
There are some possibilities, hardware-based or software-based, to improve the imaging
speed. One way is to speed up the scanning process by acquiring fewer measurements. A
recently developed mathematical framework called compressed sensing shows that it is
possible to accurately recover undersampled images provided a suitable measurement matrix
is used and the image itself has a sparse representation.
Nevertheless, not only measurements are important but also good reconstruction models
are required. Such models are usually expressed as optimization problems.
In this thesis, we concentrated on the reconstruction of the undersampled Magnetic
Resonance (MR) images. For this purpose a complex-valued reconstruction model was
provided. Since the reconstruction should be as quick as possible, fast methods to find the
solution for the reconstruction problem are required. To meet this objective, three popular
algorithms FISTA, Augmented Lagrangian and Non-linear Conjugate Gradient were adopted
to work with our model.
By changing the complex-valued reconstruction model slightly and dualizing the problem,
we obtained an instance of the quadratically constrained quadratic program where both the
objective function and the constraints are twice differentiable. Hence new model opened
doors to two other methods, the first order method which resembles FISTA and is called
in this thesis Normed Constrained Quadratic FGP, and the second order method called
Truncated Newton Primal Dual Interior Point.
Next, in order to compare performance of the methods, we set up the experiments and
evaluated all presented methods against the problem of reconstructing undersampled MR
images. In the experiments we used a number of invocations of the Fourier transform to
measure the performance of all algorithms.
As a result of the experiments we found that in the context of the original model the
performance of Augmented Lagrangian is better than the other two methods. Performance
of Non-linear Conjugate Gradient and FISTA are about the same. In the context of the
extended model Normed Constrained Quadratic FGP beats the Truncated Newton Primal
Dual Interior Point method.

A universally fastest algorithm for Max 2-Sat, Max 2-CSP, and everything in between

by Serge Gaspers

Serge Gaspers and Gregory B. Sorkin.
A universally fastest algorithm for Max 2-Sat, Max 2-CSP, and everything in between.
20th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2009),
606–615. SIAM, 2009.

We introduce "hybrid" Max 2-CSP formulas consisting of "simple clauses", namely conjunctions and... more We introduce "hybrid" Max 2-CSP formulas consisting of "simple clauses", namely conjunctions and disjunctions of pairs of variables, and general 2-variable clauses, which can be any integer-valued functions of pairs of boolean variables. This allows an algorithm to use both efficient reductions specific to AND and OR clauses, and other powerful reductions that require the general CSP setting.
Parametrizing an instance by the fraction p of nonsimple clauses, we give an exact (exponential-time) algorithm that is the fastest polynomial-space algorithm known for Max 2-Sat (and other p = 0 formulas, with arbitrary mixtures of AND and OR clauses); the only efficient algorithm for mixtures of AND, OR, and general integer-valued clauses; and tied for fastest for general Max 2-CSP (p = 1). Since a pure 2-Sat input instance may be transformed to a general CSP instance in the course of being solved, the algorithm's efficiency and generality go hand in hand.
Our novel analysis results in a family of running-time bounds, each optimized for a particular value of p. The algorithm uses new reductions introduced here, as well as recent reductions such as "clause-learning" and "2-reductions" adapted to our setting's mixture of simple and general clauses. Each reduction imposes constraints on various parameters, and the running-time bound is an "objective function" of these parameters and p. The optimal running-time bound is obtained by solving a convex nonlinear program, which can be done efficiently and with a certificate of optimality.

Classification with Specified Error Rates

by Om Patri

Technical Report, Department of Computer Science and Engineering, IIT Guwahati. As part of Computer Science Seminar course.

There are many real-world datasets which have di fferent costs for misclassifi cation of di fferent classes. Further,... more There are many real-world datasets which have different costs for misclassification of different classes. Further, the training data is usually imbalanced in such datasets. Traditional classification methods like support vector machines (SVMs) do not deal with such problems well enough. We have studied a new maximum margin classification formulation for problems with specfiied false negative and false positive error rates. Given the first and second order moments of the class conditional densities, the key idea is to use the Chebyshev-Cantelli inequality to convert the probabilistic chance constraints into second order cone constraints, thus obtaining a second order cone programming (SOCP) formulation. The dual of this formulation has an elegant geometric interpretation viz. minimizing the distance between two ellipsoids. This geometric optimization problem can be solved by a fast
iterative algorithm. The formulation is extended to non-linear feature
spaces using kernel methods.

Kernel-Based Data Fusion for Gene Prioritization

by Tijl De Bie

Gaussian Processes for Active Sensor Management

by Tijl De Bie

Discriminative Sequence Labeling by Z-Score Optimization

by Tijl De Bie

Finding Interesting Itemsets Using a Probabilistic Model for Binary Databases

by Tijl De Bie

Semi-Supervised Learning Based on Kernel Methods and Graph Cut Algorithms

by Tijl De Bie

Deploying SDP for Machine Learning

by Tijl De Bie

Explicit Probabilistic Models for Databases and Networks

by Tijl De Bie

Magic Moments for Structured Output Prediction

by Tijl De Bie

Learning to Align: a Statistical Approach

by Tijl De Bie

An Information-Theoretic Approach to Finding Informative Noisy Tiles In Binary Databases

by Tijl De Bie

A Metamorphosis of Canonical Correlation Analysis Into Multivariate Maximum Margin Learning

by Tijl De Bie

Convex Tuning of the Soft Margin Parameter

by Tijl De Bie