4 research outputs found
The Predicted-Deletion Dynamic Model: Taking Advantage of ML Predictions, for Free
The main bottleneck in designing efficient dynamic algorithms is the unknown
nature of the update sequence. In particular, there are some problems, like
3-vertex connectivity, planar digraph all pairs shortest paths, and others,
where the separation in runtime between the best partially dynamic solutions
and the best fully dynamic solutions is polynomial, sometimes even exponential.
In this paper, we formulate the predicted-deletion dynamic model, motivated
by a recent line of empirical work about predicting edge updates in dynamic
graphs. In this model, edges are inserted and deleted online, and when an edge
is inserted, it is accompanied by a "prediction" of its deletion time. This
models real world settings where services may have access to historical data or
other information about an input and can subsequently use such information make
predictions about user behavior. The model is also of theoretical interest, as
it interpolates between the partially dynamic and fully dynamic settings, and
provides a natural extension of the algorithms with predictions paradigm to the
dynamic setting.
We give a novel framework for this model that "lifts" partially dynamic
algorithms into the fully dynamic setting with little overhead. We use our
framework to obtain improved efficiency bounds over the state-of-the-art
dynamic algorithms for a variety of problems. In particular, we design
algorithms that have amortized update time that scales with a partially dynamic
algorithm, with high probability, when the predictions are of high quality. On
the flip side, our algorithms do no worse than existing fully-dynamic
algorithms when the predictions are of low quality. Furthermore, our algorithms
exhibit a graceful trade-off between the two cases. Thus, we are able to take
advantage of ML predictions asymptotically "for free.'
The Burer-Monteiro SDP method can fail even above the Barvinok-Pataki bound
The most widely used technique for solving large-scale semidefinite programs
(SDPs) in practice is the non-convex Burer-Monteiro method, which explicitly
maintains a low-rank SDP solution for memory efficiency. There has been much
recent interest in obtaining a better theoretical understanding of the
Burer-Monteiro method. When the maximum allowed rank of the SDP solution is
above the Barvinok-Pataki bound (where a globally optimal solution of rank at
most is guaranteed to exist), a recent line of work established convergence
to a global optimum for generic or smoothed instances of the problem. However,
it was open whether there even exists an instance in this regime where the
Burer-Monteiro method fails. We prove that the Burer-Monteiro method can fail
for the Max-Cut SDP on vertices when the rank is above the Barvinok-Pataki
bound (). We provide a family of instances that have spurious
local minima even when the rank . Combined with existing guarantees,
this settles the question of the existence of spurious local minima for the
Max-Cut formulation in all ranges of the rank and justifies the use of beyond
worst-case paradigms like smoothed analysis to obtain guarantees for the
Burer-Monteiro method
Management of donor-specific antibodies in lung transplantation
The formation of antibodies against donor human leukocyte antigens poses a challenging problem both for donor selection as well as postoperative graft function in lung transplantation. These donor-specific antibodies limit the pool of potential donor organs and are associated with episodes of antibody-mediated rejection, chronic lung allograft dysfunction, and increased mortality. Optimal management strategies for clearance of DSAs are poorly defined and vary greatly by institution; most of the data supporting any particular strategy is limited to small-scale retrospective cohort studies. A typical approach to antibody depletion may involve the use of high-dose steroids, plasma exchange, intravenous immunoglobulin, and possibly other immunomodulators or small-molecule therapies. This review seeks to define the current understanding of the significance of DSAs in lung transplantation and outline the literature supporting strategies for their management