Mihailo's scientific webpage
Welcome to my scientific webpage. Here you can get a bit of a preview as to how my scientific journey looks like. In short, I work in a variety of scientific fields; almost all of them either originate from mathematics or are tightly connected and in a way are converging back to mathematics. Below is a selection of some of my very best scientific achievements accompanied with a few basic details related to my interests and experiences.
Education
Ph.D., Caltech, 2008
Research interests
Fairly general, mathematics and its engineering applications
AI, machine learning, and neural networks
Probability and statistics
Design and performance analysis of optimization algorithms
Compressed sensing;, signal processing;, and information theory
Statistical mechanics; quantum physics
Econometrics
Papers
Clicking on the link to the right of each paper's titile opens the window with the abstract and from there clicking on the pdf opens the paper itself.
Journals:
M. Stojnic, ``Ground state energies of multipartite p-spin models -- partially lifted RDT view". (link)
M. Stojnic, ``CLuP practically achieves ~1.77 positive and ~0.33 negative Hopfield model ground state free energy". (link)
M. Stojnic, ``A CLuP algorithm to practically achieve ~0.76 SK--model ground state free energy". (link)
M. Caner, A. Capponi, and M. Stojnic, ``A General Class of Model-Free Dense Precision Matrix Estimators". (link)
M. Stojnic, ``Rare dense solutions clusters in asymmetric binary perceptrons -- local entropy via fully lifted RDT". (link)
M. Stojnic, ``A large deviation view of \emph{stationarized} fully lifted blirp interpolation". (link)
M. Stojnic, ``Fully lifted \emph{blirp} interpolation -- a large deviation view". (link)
M. Stojnic, ``Phase retrieval with rank d measurements -- \emph{descending} algorithms phase transitions". (link)
M. Stojnic, ``Optimal spectral initializers impact on phase retrieval phase transitions -- an RDT view ". (link)
M. Stojnic, ``Phase transition of \emph{descending} phase retrieval algorithms ". (link)
M. Stojnic, ``Deep ReLU networks -- injectivity capacity upper bounds". (link)
M. Stojnic, ``Injectivity capacity of ReLU gates". (link)
M. Stojnic, ``Theoretical limits of descending l0 sparse-regression ML algorithms". (link)
A. Capponi and M. Stojnic, ``Sparse vector and low rank recovery phase transitions: uncovering the explicit relations". (link)
M. Stojnic, ``Precise analysis of ridge interpolators under heavy correlations -- a Random Duality Theory view". (link)
M. Stojnic, ``Ridge interpolators in correlated factor regression models -- exact risk analysis". (link)
M. Stojnic, ``Exact objectives of random linear programs and mean widths of random polyhedrons". (link)
M. Stojnic, ``Capacity of the Hebbian-Hopfield network associative memory". (link)
M. Stojnic, ``Exact capacity of the \emph{wide} hidden layer treelike neural networks with generic activations". (link)
M. Stojnic, ``Fixed width treelike neural networks capacity analysis -- generic activations". (link)
A. Capponi and M. Stojnic, ``Exact Error in Matrix Completion: Approximately Low-Rank Structures and Missing Blocks". (link)
M. Stojnic, ``Fl RDT based ultimate lowering of the negative spherical perceptron capacity". (link)
M. Stojnic, ``\emph{Lifted} RDT based capacity analysis of the 1-hidden layer treelike \emph{sign} perceptrons neural networks". (link)
M. Stojnic, ``Capacity of the treelike sign perceptrons neural networks with one hidden layer -- RDT based upper bounds". (link)
M. Stojnic, ``Binary perceptrons capacity via fully lifted random duality theory". (link)
M. Stojnic, ``Studying Hopfield models via fully lifted random duality theory". (link)
M. Stojnic, ``Fully lifted random duality theory". (link)
M. Stojnic, ``Generic proving of replica symmetry breaking". (link)
M. Stojnic, ``Bilinearly indexed random processes -- \emph{stationarization} of fully lifted interpolation". (link)
M. Stojnic, ``Fully lifted interpolating comparisons of bilinearly indexed random processes". (link)
A. Capponi and M. Stojnic, ``Causal Inference (C-inf) -- asymmetric scenario of typical phase transitions". (link)
A. Capponi and M. Stojnic, ``Causal Inference (C-inf) -- closed form worst case typical phase transitions". (link)
M. Stojnic, ``Sparse linear regression -- CLuP achieves the ideal \emph{exact} ML ". (link)
M. Stojnic, ``Rephased CLuP ". (link)
M. Stojnic, ``Algorithmic random duality theory -- large scale CLuP ". (link)
M. Stojnic, ``Starting CLuP with polytope relaxation". (link)
M. Stojnic, ``Complexity analysis of the Controlled Loosening-up (CLuP) algorithm". (link)
M. Stojnic, ``Controlled Loosening-up (CLuP) -- achieving exact MIMO ML in polynomial time". (link)
M. Stojnic, ``Fully bilinear generic and lifted random processes comparisons". (link)
M. Stojnic, ``Generic and lifted probabilistic comparisons -- max replaces minmax". (link)
M. Stojnic, ``Partial ℓ1 optimization in random linear systems -- finite dimensions". (link)
M. Stojnic, ``Partial ℓ1 optimization in random linear systems -- phase transitions and large deviations". (link)
M. Stojnic, ``Box constrained ℓ1 optimization in random linear systems -- finite dimensions". (link)
M. Stojnic, ``Box constrained ℓ1 optimization in random linear systems -- asymptotics". (link)
M. Stojnic, ``Random linear under-determined systems with block-sparse solutions -- asymptotics, large deviations, and finite dimensions". (link)
M. Stojnic, ``Random linear systems with sparse solutions -- asymptotics and large deviations". (link)
M. Stojnic, ``Random linear systems with sparse solutions -- finite dimensions". (link)
M. Stojnic, ``Discrete perceptrons". (link)
M. Stojnic, ``Spherical perceptron as a storage memory with limited errors". (link)
M. Stojnic, ``Negative spherical perceptron". (link)
M. Stojnic, ``Another look at the Gardner problem". (link)
M. Stojnic, ``Asymmetric Little model and its ground state energies". (link)
M. Stojnic, ``Towards a better compressed sensing". (link)
M. Stojnic, ``Compressed sensing of block-sparse positive vectors". (link)
M. Stojnic, ``Bounds on restricted isometry constants of random matrices". (link)
M. Stojnic, ``Upper-bounding $\ell_1$-optimization sectional thresholds". (link)
M. Stojnic, ``Lifting $\ell_q$-optimization thresholds". (link)
M. Stojnic, ``Under-determined linear systems and $\ell_q$-optimization thresholds". (link)
M. Stojnic, ``Lifting $\ell_1$-optimization strong and sectional thresholds". (link)
M. Stojnic, ``Lifting/lowering Hopfield models ground state energies". (link)
M. Stojnic, ``Bounding ground state energy of Hopfield models". (link)
M. Stojnic, ``Linear under-determined systems with sparse solutions: Redirecting a challenge?". (link)
M. Stojnic, ``Regularly random duality". (link)
M. Stojnic, ``Meshes that trap random subspaces". (link)
M. Stojnic, ``A problem dependent analysis of SOCP algorithms in noisy compressed sensing". (link)
M. Stojnic, ``A performance analysis framework for SOCP algorithms in noisy compressed sensing". (link)
M. Stojnic, ``A framework to characterize performance of LASSO algorithms". (link)
M. Stojnic, ``Optimality of $\ell_2/\ell_1$-optimization block-length dependent thresholds". (link)
M. Stojnic, ``Upper-bounding $\ell_1$-optimization weak thresholds". (link)
M. Stojnic, ``A rigorous geometry-probability equivalence in characterization of $\ell_1$-optimization". (link)
M. Stojnic, ``Block-length dependent thresholds in block-sparse compressed sensing". (link)
M. Stojnic, ``Various thresholds for $\ell_1$ optimization in compressed sensing". (link)
M. Stojnic, ``$\ell_2/\ell_1$-optimization in block-sparse compressed sensing and its strong thresholds". (link)
M. Stojnic, F. Parvaresh, and B. Hassibi, ``On the reconstruction of block-sparse signals with an optimal number of measurements". (link)
M. Stojnic, H. Vikalo, and B. Hassibi, ``Speeding up the sphere decoder with $H^{\infty}$ and $SDP$ inspired lower bounds". (link)
M. Stojnic, H. Vikalo, and B. Hassibi, ``Rate maximization in multi-antenna broadcast channels using linear preprocessing". (link)
Y. Eldar, M. Stojnic, and B. Hassibi, ``Optimal quantum detectors for unambiguous detection of mixed states". (link)
Conferences:
A. Capponi and M. Stojnic, ``Phase Transitions: Explicit relations for sparse vector and low rank recovery". (link)
A. Capponi and M. Stojnic, ``Causal Inference — closed form expressions for worst case typical phase transitions". (link)
M. Stojnic, ``Recovery thresholds for $\ell_1$ optimization in binary compressed sensing". (link)
M. Stojnic, ``Towards improving $\ell_1$ optimization in compressed sensing". (link)
M. Stojnic, ``Block-length dependent thresholds for $\ell_2/\ell_1$-optimization in block-sparse compressed sensing". (link)
M. Stojnic, ``$\ell_1$ optimization and its various thresholds in compressed sensing". (link)
M. Stojnic, ``A smoothed analysis approach to $\ell_1$ optimization in compressed sensing". (link)
M. Stojnic, ``Explicit thresholds for approximately sparse compressed sensing via ℓ1-optimization". (link)
M. Stojnic, ``$\ell_2/\ell_1$-optimization and its strong thresholds in approximately block-sparse compressed sensing". (link)
M. Stojnic, ``Strong thresholds for $\ell_2/\ell_1$-optimization in block-sparse compressed sensing". (link)
M. Stojnic, ``A simple performance analysis of $\ell_1$ optimization in compressed sensing". (link)
M. Stojnic, W. Xu, and B. Hassibi, ``Compressed sensing of approximately sparse signals". (link)
W. Xu, M. Stojnic, and B. Hassibi, ``On Exact Maximum-likelihood Detection for Non-coherent MIMO Wireless Systems: A Branch-Estimate-Bound Optimization Framework". (link)
M. Stojnic, W. Xu, and B. Hassibi, ``Compressed sensing - Probabilistic analysis of a null-space characterization". (link)
W. Xu, M. Stojnic, and B. Hassibi, ``Low-complexity blind maximum-likelihood detection for SIMO systems with general constellations". (link)
M. Stojnic and B. Hassibi, ``Out-sphere decoder for non-coherent ML SIMO detection and its expected complexity". (link)
M. Stojnic and B. Hassibi, ``Unambiguous discrimination between two rank-2 mixed quantum states". (link)
M. Stojnic, B. Hassibi, and H. Vikalo, ``PEP analysis of SDP-based non-coherent signal detection". (link)
H. Vikalo, B. Hassibi, M. Stojnic, and A. Hassibi, ``Modeling the kinetics of hybridization in micro-arrays". (link)
M. Stojnic, B. Hassibi, and H. Vikalo, ``PEP analysis of SDP-based joint channel estimation and signal detection". (link)
M. Stojnic, H. Vikalo, and B. Hassibi, ``Asymptotic analysis of the Gaussian broadcast channel with perturbation preprocessing". (link)
M. Stojnic, H. Vikalo, and B. Hassibi, ``Further results on speeding up the sphere decoder". (link)
M. Stojnic, H. Vikalo, and B. Hassibi, ``An efficient $H^{\infty}$ estimation approach to speed up the sphere decoder". (link)
M. Stojnic, H. Vikalo, and B. Hassibi, ``An $H^{\infty}$-based lower bound to speed up the sphere decoder". (link)
M. Stojnic, H. Vikalo, and B. Hassibi, ``A branch and bound approach to speed up the sphere decoder". (link)
M. Stojnic, H. Vikalo, and B. Hassibi, ``Rate maximization in multi-antenna broadcast channels using linear preprocessing". (link)