134 research outputs found
Forbidden Directed Minors and Kelly-width
Partial 1-trees are undirected graphs of treewidth at most one. Similarly,
partial 1-DAGs are directed graphs of KellyWidth at most two. It is well-known
that an undirected graph is a partial 1-tree if and only if it has no K_3
minor. In this paper, we generalize this characterization to partial 1-DAGs. We
show that partial 1-DAGs are characterized by three forbidden directed minors,
K_3, N_4 and M_5
Optimal Scalarizations for Sublinear Hypervolume Regret
Scalarization is a general technique that can be deployed in any
multiobjective setting to reduce multiple objectives into one, such as recently
in RLHF for training reward models that align human preferences. Yet some have
dismissed this classical approach because linear scalarizations are known to
miss concave regions of the Pareto frontier. To that end, we aim to find simple
non-linear scalarizations that can explore a diverse set of objectives on
the Pareto frontier, as measured by the dominated hypervolume. We show that
hypervolume scalarizations with uniformly random weights are surprisingly
optimal for provably minimizing the hypervolume regret, achieving an optimal
sublinear regret bound of , with matching lower bounds that
preclude any algorithm from doing better asymptotically. As a theoretical case
study, we consider the multiobjective stochastic linear bandits problem and
demonstrate that by exploiting the sublinear regret bounds of the hypervolume
scalarizations, we can derive a novel non-Euclidean analysis that produces
improved hypervolume regret bounds of . We
support our theory with strong empirical performance of using simple
hypervolume scalarizations that consistently outperforms both the linear and
Chebyshev scalarizations, as well as standard multiobjective algorithms in
bayesian optimization, such as EHVI.Comment: ICML 2023 Worksho
Loan Loss Provisioning in Chinese Commercial Banks
The object of this paper is to jointly test the existence of income smoothing, capital management behavior and procyclicality with respect to Chinese commercial banks' provisioning during 2009-2014. Our results provide evidence for income smoothing behavior and procyclical provisioning, but we find no evidence for capital management behavior. In order to address the problems of income smoothing and procyclical provisioning, we give the following suggestions. Bank regulators should further promote the implementation of Basel III regimes among Chinese commercial banks. The dynamic provisioning practice should be promoted and the accounting disclosure requirements should be improved. Besides, bank regulators should require banks to write off uncollectible loans in time and should also strengthen the supervision and scrutiny of banks' activities
Optimal Query Complexities for Dynamic Trace Estimation
We consider the problem of minimizing the number of matrix-vector queries
needed for accurate trace estimation in the dynamic setting where our
underlying matrix is changing slowly, such as during an optimization process.
Specifically, for any matrices with consecutive differences
bounded in Schatten- norm by , we provide a novel binary tree
summation procedure that simultaneously estimates all traces up to
error with failure probability with an optimal query
complexity of , improving the dependence on both and
from Dharangutte and Musco (NeurIPS, 2021). Our procedure works without
additional norm bounds on and can be generalized to a bound for the
-th Schatten norm for , giving a complexity of
.
By using novel reductions to communication complexity and
information-theoretic analyses of Gaussian matrices, we provide matching lower
bounds for static and dynamic trace estimation in all relevant parameters,
including the failure probability. Our lower bounds (1) give the first tight
bounds for Hutchinson's estimator in the matrix-vector product model with
Frobenius norm error even in the static setting, and (2) are the first
unconditional lower bounds for dynamic trace estimation, resolving open
questions of prior work.Comment: 30 page
New Absolute Fast Converging Phylogeny Estimation Methods with Improved Scalability and Accuracy
Absolute fast converging (AFC) phylogeny estimation methods are ones that have been proven to recover the true tree with high probability given sequences whose lengths are polynomial in the number of number of leaves in the tree (once the shortest and longest branch lengths are fixed). While there has been a large literature on AFC methods, the best in terms of empirical performance was DCM_NJ, published in SODA 2001. The main empirical advantage of DCM_NJ over other AFC methods is its use of neighbor joining (NJ) to construct trees on smaller taxon subsets, which are then combined into a tree on the full set of species using a supertree method; in contrast, the other AFC methods in essence depend on quartet trees that are computed independently of each other, which reduces accuracy compared to neighbor joining. However, DCM_NJ is unlikely to scale to large datasets due to its reliance on supertree methods, as no current supertree methods are able to scale to large datasets with high accuracy. In this study we present a new approach to large-scale phylogeny estimation that shares some of the features of DCM_NJ but bypasses the use of supertree methods. We prove that this new approach is AFC and uses polynomial time. Furthermore, we describe variations on this basic approach that can be used with leaf-disjoint constraint trees (computed using methods such as maximum likelihood) to produce other AFC methods that are likely to provide even better accuracy. Thus, we present a new generalizable technique for large-scale tree estimation that is designed to improve scalability for phylogeny estimation methods to ultra-large datasets, and that can be used in a variety of settings (including tree estimation from unaligned sequences, and species tree estimation from gene trees)
Leveraging Contextual Counterfactuals Toward Belief Calibration
Beliefs and values are increasingly being incorporated into our AI systems
through alignment processes, such as carefully curating data collection
principles or regularizing the loss function used for training. However, the
meta-alignment problem is that these human beliefs are diverse and not aligned
across populations; furthermore, the implicit strength of each belief may not
be well calibrated even among humans, especially when trying to generalize
across contexts. Specifically, in high regret situations, we observe that
contextual counterfactuals and recourse costs are particularly important in
updating a decision maker's beliefs and the strengths to which such beliefs are
held. Therefore, we argue that including counterfactuals is key to an accurate
calibration of beliefs during alignment. To do this, we first segment belief
diversity into two categories: subjectivity (across individuals within a
population) and epistemic uncertainty (within an individual across different
contexts). By leveraging our notion of epistemic uncertainty, we introduce `the
belief calibration cycle' framework to more holistically calibrate this
diversity of beliefs with context-driven counterfactual reasoning by using a
multi-objective optimization. We empirically apply our framework for finding a
Pareto frontier of clustered optimal belief strengths that generalize across
different contexts, demonstrating its efficacy on a toy dataset for credit
decisions.Comment: ICML (International Conference on Machine Learning) Workshop on
Counterfactuals in Minds and Machines, 202
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