25,677 research outputs found
A Method for Estimating the Probability of Extremely Rare Accidents in Complex Systems
Estimating the probability of failures or accidents with aerospace systems is
often necessary when new concepts or designs are introduced, as it is being
done for Autonomous Aircraft. If the design is safe, as it is supposed to be,
accident cases are hard to find. Such analysis needs some variance reduction
technique and several algorithms exist for that, however specific model
features may cause difficulties in practice, such as the case of system models
where independent agents have to autonomously accomplish missions within finite
time, and likely with the presence of human agents. For handling these
scenarios, this paper presents a novel estimation approach, based on the
combination of the well-established variation reduction technique of
Interacting Particles System (IPS) with the long-standing optimization
algorithm denominated DIviding RECTangles (DIRECT). When combined, these two
techniques yield statistically significant results for extremely low
probabilities. In addition, this novel approach allows the identification of
intermediate events and simplifies the evaluation of sensitivity of the
estimated probabilities to certain system parameters
The Partially Observable Hidden Markov Model and its Application to Keystroke Dynamics
The partially observable hidden Markov model is an extension of the hidden
Markov Model in which the hidden state is conditioned on an independent Markov
chain. This structure is motivated by the presence of discrete metadata, such
as an event type, that may partially reveal the hidden state but itself
emanates from a separate process. Such a scenario is encountered in keystroke
dynamics whereby a user's typing behavior is dependent on the text that is
typed. Under the assumption that the user can be in either an active or passive
state of typing, the keyboard key names are event types that partially reveal
the hidden state due to the presence of relatively longer time intervals
between words and sentences than between letters of a word. Using five public
datasets, the proposed model is shown to consistently outperform other anomaly
detectors, including the standard HMM, in biometric identification and
verification tasks and is generally preferred over the HMM in a Monte Carlo
goodness of fit test
Reliable uncertainties in indirect measurements
In this article we present very intuitive, easy to follow, yet mathematically
rigorous, approach to the so called data fitting process. Rather than
minimizing the distance between measured and simulated data points, we prefer
to find such an area in searched parameters' space that generates simulated
curve crossing as many acquired experimental points as possible, but at least
half of them. Such a task is pretty easy to attack with interval calculations.
The problem is, however, that interval calculations operate on guaranteed
intervals, that is on pairs of numbers determining minimal and maximal values
of measured quantity while in vast majority of cases our measured quantities
are expressed rather as a pair of two other numbers: the average value and its
standard deviation. Here we propose the combination of interval calculus with
basic notions from probability and statistics. This approach makes possible to
obtain the results in familiar form as reliable values of searched parameters,
their standard deviations, and their correlations as well. There are no
assumptions concerning the probability density distributions of experimental
values besides the obvious one that their variances are finite. Neither the
symmetry of uncertainties of experimental distributions is required (assumed)
nor those uncertainties have to be `small.' As a side effect, outliers are
quietly and safely ignored, even if numerous.Comment: 9 pages, 4 figures, PACS numbers: 07.05.Kf; 02.60.Ed; 02.70.R
Counterfactual Reasoning and Learning Systems
This work shows how to leverage causal inference to understand the behavior
of complex learning systems interacting with their environment and predict the
consequences of changes to the system. Such predictions allow both humans and
algorithms to select changes that improve both the short-term and long-term
performance of such systems. This work is illustrated by experiments carried
out on the ad placement system associated with the Bing search engine.Comment: revised versio
Local optimization-based statistical inference
This paper introduces a local optimization-based approach to test statistical
hypotheses and to construct confidence intervals. This approach can be viewed
as an extension of bootstrap, and yields asymptotically valid tests and
confidence intervals as long as there exist consistent estimators of unknown
parameters. We present simple algorithms including a neighborhood bootstrap
method to implement the approach. Several examples in which theoretical
analysis is not easy are presented to show the effectiveness of the proposed
approach
Active Ranking from Pairwise Comparisons and when Parametric Assumptions Don't Help
We consider sequential or active ranking of a set of n items based on noisy
pairwise comparisons. Items are ranked according to the probability that a
given item beats a randomly chosen item, and ranking refers to partitioning the
items into sets of pre-specified sizes according to their scores. This notion
of ranking includes as special cases the identification of the top-k items and
the total ordering of the items. We first analyze a sequential ranking
algorithm that counts the number of comparisons won, and uses these counts to
decide whether to stop, or to compare another pair of items, chosen based on
confidence intervals specified by the data collected up to that point. We prove
that this algorithm succeeds in recovering the ranking using a number of
comparisons that is optimal up to logarithmic factors. This guarantee does not
require any structural properties of the underlying pairwise probability
matrix, unlike a significant body of past work on pairwise ranking based on
parametric models such as the Thurstone or Bradley-Terry-Luce models. It has
been a long-standing open question as to whether or not imposing these
parametric assumptions allows for improved ranking algorithms. For stochastic
comparison models, in which the pairwise probabilities are bounded away from
zero, our second contribution is to resolve this issue by proving a lower bound
for parametric models. This shows, perhaps surprisingly, that these popular
parametric modeling choices offer at most logarithmic gains for stochastic
comparisons.Comment: improved log factor in main result; added discussion on comparison
probabilities close to zero; added numerical result
Algorithms for Linear Bandits on Polyhedral Sets
We study stochastic linear optimization problem with bandit feedback. The set
of arms take values in an -dimensional space and belong to a bounded
polyhedron described by finitely many linear inequalities. We provide a lower
bound for the expected regret that scales as . We then provide
a nearly optimal algorithm and show that its expected regret scales as
for an arbitrary small . The algorithm
alternates between exploration and exploitation intervals sequentially where
deterministic set of arms are played in the exploration intervals and greedily
selected arm is played in the exploitation intervals. We also develop an
algorithm that achieves the optimal regret when sub-Gaussianity parameter of
the noise term is known. Our key insight is that for a polyhedron the optimal
arm is robust to small perturbations in the reward function. Consequently, a
greedily selected arm is guaranteed to be optimal when the estimation error
falls below some suitable threshold. Our solution resolves a question posed by
Rusmevichientong and Tsitsiklis (2011) that left open the possibility of
efficient algorithms with asymptotic logarithmic regret bounds. We also show
that the regret upper bounds hold with probability . Our numerical
investigations show that while theoretical results are asymptotic the
performance of our algorithms compares favorably to state-of-the-art algorithms
in finite time as well
Locally Private Mean Estimation: Z-test and Tight Confidence Intervals
This work provides tight upper- and lower-bounds for the problem of mean
estimation under -differential privacy in the local model, when the
input is composed of i.i.d. drawn samples from a normal distribution with
variance . Our algorithms result in a -confidence interval
for the underlying distribution's mean of length . In
addition, our algorithms leverage binary search using local differential
privacy for quantile estimation, a result which may be of separate interest.
Moreover, we prove a matching lower-bound (up to poly-log factors), showing
that any one-shot (each individual is presented with a single query) local
differentially private algorithm must return an interval of length
Rarely-switching linear bandits: optimization of causal effects for the real world
Excessively changing policies in many real world scenarios is difficult,
unethical, or expensive. After all, doctor guidelines, tax codes, and price
lists can only be reprinted so often. We may thus want to only change a policy
when it is probable that the change is beneficial. In cases that a policy is a
threshold on contextual variables we can estimate treatment effects for
populations lying at the threshold. This allows for a schedule of incremental
policy updates that let us optimize a policy while making few detrimental
changes. Using this idea, and the theory of linear contextual bandits, we
present a conservative policy updating procedure which updates a deterministic
policy only when justified. We extend the theory of linear bandits to this
rarely-switching case, proving that such procedures share the same regret, up
to constant scaling, as the common LinUCB algorithm. However the algorithm
makes far fewer changes to its policy and, of those changes, fewer are
detrimental. We provide simulations and an analysis of an infant health
well-being causal inference dataset, showing the algorithm efficiently learns a
good policy with few changes. Our approach allows efficiently solving problems
where changes are to be avoided, with potential applications in medicine,
economics and beyond.Comment: 17 pages, 9 figure
Adaptive, Distribution-Free Prediction Intervals for Deep Networks
The machine learning literature contains several constructions for prediction
intervals that are intuitively reasonable but ultimately ad-hoc in that they do
not come with provable performance guarantees. We present methods from the
statistics literature that can be used efficiently with neural networks under
minimal assumptions with guaranteed performance. We propose a neural network
that outputs three values instead of a single point estimate and optimizes a
loss function motivated by the standard quantile regression loss. We provide
two prediction interval methods with finite sample coverage guarantees solely
under the assumption that the observations are independent and identically
distributed. The first method leverages the conformal inference framework and
provides average coverage. The second method provides a new, stronger guarantee
by conditioning on the observed data. Lastly, our loss function does not
compromise the predictive accuracy of the network like other prediction
interval methods. We demonstrate the ease of use of our procedures as well as
its improvements over other methods on both simulated and real data. As most
deep networks can easily be modified by our method to output predictions with
valid prediction intervals, its use should become standard practice, much like
reporting standard errors along with mean estimates
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