The second season of the smash hit sci-fi drama Severancefinally premieres on January 17. However, Apple just threw us a bone by dropping the first eight minutes of the season. It’s been nearly three years since season one completed its run, so this is a nice little holiday gift.
You can find the exclusive preview on the Apple TV+ app under the Bonus Content section of the Severance page. There will be no spoilers here, but the snippet does get into the fallout of the events of season one and may even touch on that surprising cliffhanger.
For the uninitiated, Severance is a sci-fi take on work/life balance in which certain employees at a shadowy corporation “sever” their work selves from their regular selves. This results in a harrowing, and occasionally hilarious, treatise about human identity and the lengths our corporate overlords will go to make a buck. It’s very good. Best of all? Newbies won’t have to wait three full years to watch season two.
Apple TV+ also just posted a bunch of images to social media that heavily imply its planning on a free weekend of sorts for non-subscribers, scheduled for January 4 and 5. The images are all tagged with slogans like “see for yourself” and “save the date.”
If true, this would be a mighty fine way to check out Apple’s impressive slate of sci-fi originals without ponying up for a subscription. The streamer has become the de facto home of sci-fi in recent years, airing standout programs like Severance, Silo, Foundation and For All Mankind, among many others.
This article originally appeared on Engadget at https://www.engadget.com/entertainment/tv-movies/apple-just-dropped-the-first-eight-minutes-of-severance-season-two-181627223.html?src=rss
I’ve lost count of the number of things we reviewed this year at Engadget. In 2024, the types of products we tested ranged from the typical phones, laptops and headphones to AI wearables, robotic lawnmowers and handheld gaming consoles, alongside games and shows. It can feel hard to keep track of it all, but thankfully, our scoring system helps us highlight the best (and the worst) devices each year.
Our team of reviewers and editors evaluate products based on their performance, value and how they hold up against the competition, and at least two people weigh in on every score before it’s published. If something gets a result of 80 and up, it’s considered a “Recommended” product, while those scoring 90 and more are awarded “Editors’ Choice.” The latter means they’re the best in their class, beating out most of the competition.
Since we have to be very judicious about what we review (there’s only so much time in the world), most of the gadgets we call in are from established companies with a track record of making things people will actually consider buying. That’s the main reason most of our scores sit between 80 and 90, though we still test the occasional device that ends up getting a number below 70.
As we look back on the year in gadgets, here are the 12 highest-scored reviews we published. Unsurprisingly, they’re mostly of Apple and Google products, with a smattering of cameras and drones. I’m also including some honorable mentions for good measure, as well as a pair of the lowest-rated devices all year. May we have only excellent gadgets to review next year, and may there be less e-waste all around.
Pixel 9 Pro and Pixel 9 Pro XL
I’m honestly shocked. For the first time in years, we’ve given a Google phone a higher score than an iPhone in the same year. Maybe it has something to do with Gemini AI launching earlier than Apple Intelligence, or the fun colors and solid build of the Pixel 9 Pro series. But as I discussed the scores with our reviewer Mat Smith, a few things added up. Arguably the biggest advantage Google has over Apple this year is battery life — the Pixel 9 Pros generally last about two days on a charge, while the iPhone 16 Pro series typically clocks just around 20 hours. We also love Google’s cameras and the bright, smooth displays. The gorgeous palette of pastel color options is just icing on a satisfying cake, with Gemini AI bringing a tasty side treat.
DJI Avata 2
Though there is looming concern over DJI’s longevity in the US, the company has otherwise had a relatively successful 2024. This year saw many DJI products scoring more than 90 in our database, which makes sense as they are arguably the best drone maker around. Steve was most impressed by the Avata 2, though, thanks to its great video quality and maneuverability for a lower price than its predecessor. It even has better battery life, to boot.
iPhone 16 Pro and iPhone 16 Pro Max
Apple Intelligence wasn’t available when the iPhone 16 series launched and only recently rolled out, so our review score might still change, But as it is, and after months of using the iPhone 16 Pro and Pro Max in my daily life, I stand by my evaluation. Though there’s a lot to like about Apple’s latest flagships, I was just so disappointed by the relatively poor battery life that I could not score it higher than the Pixel 9 Pro series. This is more noticeable on the iPhone 16 Pro, though, as the Pro Max generally lasts a few more hours than its smaller counterpart. I also wish the generative-AI features were ready for the public at the time of my review, but now that I’ve spent more time with Genmoji, Image Playground and notification summaries, I’m pretty sure my verdict remains the same. These Apple Intelligence features are fun, but not game-changing, and with or without them the iPhone 16 Pro and Pro Max are still the best options for anyone on iOS.
Canon EOS R5 II
We’ve got a slew of reviews by Steve on this list, mostly for products in cameras and drones that ranked well in their categories. As a Canon girl myself, I was happy to see the EOS R5 II get such a good rating, especially since competition has been heating up. Sadly, the EOS R5 II also heats up when shooting high-res video, but on pretty much every other aspect, it performs respectably. According to Steve, this camera “puts Sony on notice,” and I’m glad to see it.
Sony A9 III
Reviewed much earlier in the year, the Sony A9 III caught Steve’s attention for its speedy global shutter, which brought fast and accurate autofocus. It also delivered smooth, high-quality video in a body with excellent handling thanks to Sony’s comfortable new grip. Steve also loved the viewfinder, and though it’s very expensive at $6,000, the A9 III is a solid product that holds the title of “fastest full-frame camera” — at least, until something faster comes along.
DJI Air 3S and DJI Neo
What lightweight $200 drone shoots good 1080p video but also screams like a banshee? That would be the DJI Neo, which, despite Steve’s evocative description, is something I’m considering buying for myself. Not only is it reasonably priced, but it also promises to capture smooth aerial footage at a respectable resolution. Steve also found it beginner-friendly, which is important for a lousy pilot like me. And sure, maybe I’ll scare some wildlife or neighbors with its loud screeching, but maybe that’s part of the fun?
If you want something that can avoid people or obstacles and deliver cinematic shots, the DJI Air 3S is a solid option thanks to its LiDAR and larger camera sensor, both of which improve performance and obstacle-detection in low light. You’ll have to pay about five times the Neo’s cost, of course, but aspiring Spielbergs might find that price worthwhile.
MacBook Pro (14-inch, 2024) and MacBook Pro (16-inch, 2024)
I’m not surprised that the only laptops to make it to this list are this year’s M4 MacBook Pros. Apple has demonstrated over the last few years that its M-series processors deliver excellent performance and battery life, and it’s continued to prove its point in 2024. This year’s model features brighter screens and improved webcams, as well as slight bumps in RAM and storage. I’m a Windows user, but even I have to admit that what Apple is doing with the MacBooks is something that Microsoft and all its partners on the PC side have struggled to fully replicate.
ASUS ROG Zephyrus G14 (2024)
What PC makers do excel at is power and creativity. When it’s not experimenting with dual-screen laptops, ASUS is pushing out capable gaming laptops in its Republic of Gamers (ROG) brand. This year, our reviewer Sam Rutherford’s top-scored product is the ROG Zephyrus G14, which he declared “the 14-inch gaming laptop to beat.” Sam hasn’t given out a higher score at all this year, so it stands to reason we have yet to see a gaming notebook steal that crown. The Zephyrus G14 won Sam over with its beautiful OLED screen, attractive yet subtle design and generous array of ports. Though he’s not a fan of its soldered-in RAM and ASUS’ Armoury Crate app, Sam still found plenty to like, calling it “both pound for pound and dollar for dollar the best choice around.”
But I wanted to shout out Daniel Cooper’s review of the reMarkable Paper Pro. It’s a gadget that’s brought back waves of nostalgia and sentimentality in a time when we’re all tired of constantly being wired in. It’s one of the highest-rated products of its kind, not only because it’s a capable writing tablet, but also because it is a color e-paper tablet that has a bigger screen and faster performance than its monochrome predecessor. At $580 to start, it’s certainly a significant investment, but one that might free us from feeling chained to our laptops and phones.
Worst products we reviewed this year: Humane AI Pin and Rabbit R1
In all my 8-plus years at Engadget, I can only remember one other time we’ve awarded anything a sub-60 score, and that was when Fisher-Price’s Sproutling wearable baby monitor gave our editor’s baby an eczema outbreak. The Sproutling got an appropriately all-time low score of 41, and this year, the Rabbit R1 broke that bottom when Devindra decided it deserved only 40 points.
The Rabbit R1 first made waves at CES 2024, when it showed up out of nowhere and enticed many of us with its cute looks and bright orange color. Its Teenage Engineering heritage was even more alluring, and we all wanted to try out the Playdate-esque scroll wheel for ourselves. The square device also came with an onboard camera, two microphones, rotating camera and a 2.88-inch display. But its biggest promise was, as with everything in 2024, all about AI.
And with many things in 2024, the AI promise fell flat. Rabbit made bold claims about its “large action model,” but in actuality, at the time of our review, the R1 could barely execute tasks to completion. Instead of letting you easily make orders via DoorDash, for example, it would “often deliver the weather when I asked for traffic,” according to Devindra’s review. Worse, “sometimes it would hear my request and simply do nothing.”
Photo by Cherlynn Low / Engadget
I had a similarly frustrating experience when testing the much-hyped Humane AI Pin. It was a shiny chrome square that you could attach to your clothes and interact with either by voice, touch or via a futuristic-looking projector that beamed a display onto your palm. You were supposed to be able to simply talk to the Humane AI assistant to get it to remember things for and about you, eventually coming to rely on it like a second brain.
Instead, we got a hot mess. Quite literally. The Humane AI Pin would frequently run so hot that it would stop working, with the device saying it needed to cool down for a bit before you could use it again. When it did work, it was barely smart enough to answer questions, and though the projector was cool visually, using it to do anything was frustrating and just led to sore arms and crossed eyes. Not only did it not do enough to justify the effort involved in using it, the Humane AI Pin also cost $700 — way too much for a product this finicky.
It gets worse (or better, depending on how you’re reading this). Shortly after it was widely criticized by reviewers in April, leaked internal documents showed that people appeared to be returning the AI Pins faster than the company was selling them. In October, Humane had to issue a recall for its charging case due to overheating, with the Consumer Product Safety Commission saying it posed “a fire hazard.”
I gave the Humane AI Pin a score of 50 in my review, in large part due to the intriguing projector display. Right now, though, it seems these AI gadgets are, at best, struggling to take hold. At worst, they’re on fire.
This article originally appeared on Engadget at https://www.engadget.com/the-12-best-gadgets-we-reviewed-this-year-173024990.html?src=rss
Beats updated its high-end flagship wireless headphones last year, bringing a slew of upgrades over the Studio 3 Wireless, the model it replaced. The Beats Studio Pro has better sound, active noise cancellation (ANC), Spatial Audio and more. But at $350, it didn’t necessarily stand out among stiff competition from Sony and Bose. Well, today at Amazon, the premium headphones have a new draw that those rivals don’t: They’re on sale for a mere $170. That’s 51 percent off and only $10 more than the record low.
Although the Beats Studio Pro doesn’t look starkly different from the Studio 3 Wireless it replaced, it adds subtle aesthetic touches like new colors, a tone-on-tone finish and UltraPlush memory foam (wrapped in leather) earpads. Of course, you still get the brand’s iconic lower-case “b” logo on each earpiece.
But the biggest changes are on the inside. Using Beats’ second-gen audio chip and new 40mm drivers with a two-layer diaphragm, micro vents and acoustic mesh, they have improved clarity and a more balanced profile than the Studio 3 Wireless. Although Beats was once known for overpowering bass at the expense of mids, highs and clarity, that’s no longer the case. Engadget’s audio guru, Billy Steele, found that the cans produced even-handed tuning and attention to precision once unheard of in the brand’s pre-Apple days.
The Studio Pro also has Spatial Audio, familiar to anyone who’s used Apple’s recent AirPods. (Bose also added its equivalent in its Ultra line.) The technology simulates 64 speakers around you, creating a more distinct separation between instruments and voices. You can choose between head-tracked and fixed modes, too. However, the digital trickery’s effectiveness can vary depending on the track, ranging from breathing new life into old tracks to hardly providing a noticeable difference in some other genres.
The headphones also let you listen to high-resolution and lossless music via USB-C wired listening — up to 24-bit / 48kHz. They also have a transparency mode, up to 40 hours of listening with ANC off (or around 24 hours with ANC or transparency mode on) and a fast-fuel feature that gives you four hours of playback after just a 10-minute charge.
If ANC isn’t your priority, you may want to look at the cheaper Beats Solo 4, also on sale. Offering better sound quality and longer battery life over the Solo 3, this 2024 model is on sale at Amazon for $100 — half off.
Follow @EngadgetDeals on Twitter and subscribe to the Engadget Deals newsletter for the latest tech deals and buying advice.
This article originally appeared on Engadget at https://www.engadget.com/deals/the-beats-studio-pro-headphones-are-half-off-right-now-172541818.html?src=rss
There are plenty of great tools out there for creative writers, but at the end of the day, Google’s free cloud-based word processor gets the job done just fine.
Introduction to the Finite Normal Mixtures in Regression with R
How to make linear regression flexible enough for non-linear data
The linear regression is usually considered not flexible enough to tackle the nonlinear data. From theoretical viewpoint it is not capable to dealing with them. However, we can make it work for us with any dataset by using finite normal mixtures in a regression model. This way it becomes a very powerful machine learning tool which can be applied to virtually any dataset, even highly non-normal with non-linear dependencies across the variables.
What makes this approach particularly interesting comes with interpretability. Despite an extremely high level of flexibility all the detected relations can be directly interpreted. The model is as general as neural network, still it does not become a black-box. You can read the relations and understand the impact of individual variables.
In this post, we demonstrate how to simulate a finite mixture model for regression using Markov Chain Monte Carlo (MCMC) sampling. We will generate data with multiple components (groups) and fit a mixture model to recover these components using Bayesian inference. This process involves regression models and mixture models, combining them with MCMC techniques for parameter estimation.
Data simulated as a mixtures of three linear regressions
Loading Required Libraries
We begin by loading the necessary libraries to work with regression models, MCMC, and multivariate distributions
# Loading the required libraries for various functions library("pscl") # For pscl specific functions, like regression models library("MCMCpack") # For MCMC sampling functions, including posterior distributions library(mvtnorm) # For multivariate normal distribution functio
pscl: Used for various statistical functions like regression models.
MCMCpack: Contains functions for Bayesian inference, particularly MCMC sampling.
mvtnorm: Provides tools for working with multivariate normal distributions.
Data Generation
We simulate a dataset where each observation belongs to one of several groups (components of the mixture model), and the response variable is generated using a regression model with random coefficients.
We consider a general setup for a regression model using G Normal mixture components.
## Generate the observations # Set the length of the time series (number of observations per group) N <- 1000 # Set the number of simulations (iterations of the MCMC process) nSim <- 200 # Set the number of components in the mixture model (G is the number of groups) G <- 3
N: The number of observations per group.
nSim: The number of MCMC iterations.
G: The number of components (groups) in our mixture model.
Simulating Data
Each group is modeled using a univariate regression model, where the explanatory variables (X) and the response variable (y) are simulated from normal distributions. The betas represent the regression coefficients for each group, and sigmas represent the variance for each group.
# Set the values for the regression coefficients (betas) for each group betas <- 1:sum(dimG) * 2.5 # Generating sequential betas with a multiplier of 2.5 # Define the variance (sigma) for each component (group) in the mixture sigmas <- rep(1, G) / 1 # Set variance to 1 for each component, with a fixed divisor of 1
betas: These are the regression coefficients. Each group’s coefficient is sequentially assigned.
sigmas: Represents the variance for each group in the mixture model.
In this model we allow each mixture component to possess its own variance paraameter and set of regression parameters.
Group Assignment and Mixing
We then simulate the group assignment of each observation using a random assignment and mix the data for all components.
We augment the model with a set of component label vectors for
where
and thus z_gi=1 implies that the i-th individual is drawn from the g-th component of the mixture.
This random assignment forms the z_original vector, representing the true group each observation belongs to.
# Initialize the original group assignments (z_original) z_original <- matrix(NA, N * G, 1) # Repeat each group label N times (assign labels to each observation per group) z_original <- rep(1:G, rep(N, G)) # Resample the data rows by random order sampled_order <- sample(nrow(data)) # Apply the resampled order to the data data <- data[sampled_order,]
Bayesian Inference: Priors and Initialization
We set prior distributions for the regression coefficients and variances. These priors will guide our Bayesian estimation.
## Define Priors for Bayesian estimation# Define the prior mean (muBeta) for the regression coefficients muBeta <- matrix(0, G, 1)# Define the prior variance (VBeta) for the regression coefficients VBeta <- 100 * diag(G) # Large variance (100) as a prior for the beta coefficients# Prior for the sigma parameters (variance of each component) ag <- 3 # Shape parameter bg <- 1/2 # Rate parameter for the prior on sigma shSigma <- ag raSigma <- bg^(-1)
muBeta: The prior mean for the regression coefficients. We set it to 0 for all components.
VBeta: The prior variance, which is large (100) to allow flexibility in the coefficients.
shSigma and raSigma: Shape and rate parameters for the prior on the variance (sigma) of each group.
For the component indicators and component probabilities we consider following prior assignment
The multinomial prior M is the multivariate generalizations of the binomial, and the Dirichlet prior D is a multivariate generalization of the beta distribution.
MCMC Initialization
In this section, we initialize the MCMC process by setting up matrices to store the samples of the regression coefficients, variances, and mixing proportions.
## Initialize MCMC sampling# Initialize matrix to store the samples for beta mBeta <- matrix(NA, nSim, G)# Assign the first value of beta using a random normal distribution for (g in 1:G) { mBeta[1, g] <- rnorm(1, muBeta[g, 1], VBeta[g, g]) }# Initialize the sigma^2 values (variance for each component) mSigma2 <- matrix(NA, nSim, G) mSigma2[1, ] <- rigamma(1, shSigma, raSigma)# Initialize the mixing proportions (pi), using a Dirichlet distribution mPi <- matrix(NA, nSim, G) alphaPrior <- rep(N/G, G) # Prior for the mixing proportions, uniform across groups mPi[1, ] <- rdirichlet(1, alphaPrior)
mBeta: Matrix to store samples of the regression coefficients.
mSigma2: Matrix to store the variances (sigma squared) for each component.
mPi: Matrix to store the mixing proportions, initialized using a Dirichlet distribution.
MCMC Sampling: Posterior Updates
If we condition on the values of the component indicator variables z, the conditional likelihood can be expressed as
In the MCMC sampling loop, we update the group assignments (z), regression coefficients (beta), and variances (sigma) based on the posterior distributions. The likelihood of each group assignment is calculated, and the group with the highest posterior probability is selected.
The following complete posterior conditionals can be obtained:
where
denotes all the parameters in our posterior other than x.
and where n_g denotes the number of observations in the g-th component of the mixture.
and
Algorithm below draws from the series of posterior distributions above in a sequential order.
## Start the MCMC iterations for posterior sampling# Loop over the number of simulations for (i in 2:nSim) { print(i) # Print the current iteration number
# For each observation, update the group assignment (z) for (t in 1:(N*G)) { fig <- NULL for (g in 1:G) { # Calculate the likelihood of each group and the corresponding posterior probability fig[g] <- dnorm(y[t, 1], X[t, ] %*% mBeta[i-1, g], sqrt(mSigma2[i-1, g])) * mPi[i-1, g] } # Avoid zero likelihood and adjust it if (all(fig) == 0) { fig <- fig + 1/G }
# Sample a new group assignment based on the posterior probabilities z[i, t] <- which(rmultinom(1, 1, fig/sum(fig)) == 1) }
# Update the regression coefficients for each group for (g in 1:G) { # Compute the posterior mean and variance for beta (using the data for group g) DBeta <- solve(t(X[z[i, ] == g, ]) %*% X[z[i, ] == g, ] / mSigma2[i-1, g] + solve(VBeta[g, g])) dBeta <- t(X[z[i, ] == g, ]) %*% y[z[i, ] == g, 1] / mSigma2[i-1, g] + solve(VBeta[g, g]) %*% muBeta[g, 1]
# Sample a new value for beta from the multivariate normal distribution mBeta[i, g] <- rmvnorm(1, DBeta %*% dBeta, DBeta)
# Update the number of observations in group g ng[i, g] <- sum(z[i, ] == g)
# Update the variance (sigma^2) for each group mSigma2[i, g] <- rigamma(1, ng[i, g]/2 + shSigma, raSigma + 1/2 * sum((y[z[i, ] == g, 1] - (X[z[i, ] == g, ] * mBeta[i, g]))^2)) }
# Reorder the group labels to maintain consistency reorderWay <- order(mBeta[i, ]) mBeta[i, ] <- mBeta[i, reorderWay] ng[i, ] <- ng[i, reorderWay] mSigma2[i, ] <- mSigma2[i, reorderWay]
# Update the mixing proportions (pi) based on the number of observations in each group mPi[i, ] <- rdirichlet(1, alphaPrior + ng[i, ]) }
This block of code performs the key steps in MCMC:
Group Assignment Update: For each observation, we calculate the likelihood of the data belonging to each group and update the group assignment accordingly.
Regression Coefficient Update: The regression coefficients for each group are updated using the posterior mean and variance, which are calculated based on the observed data.
Variance Update: The variance of the response variable for each group is updated using the inverse gamma distribution.
Visualizing the Results
Finally, we visualize the results of the MCMC sampling. We plot the posterior distributions for each regression coefficient, compare them to the true values, and plot the most likely group assignments.
# Plot the posterior distributions for each beta coefficient par(mfrow=c(G,1)) for (g in 1:G) { plot(density(mBeta[5:nSim, g]), main = 'True parameter (vertical) and the distribution of the samples') # Plot the density for the beta estimates abline(v = betas[g]) # Add a vertical line at the true value of beta for comparison }
This plot shows how the MCMC samples (posterior distribution) for the regression coefficients converge to the true values (betas).
Conclusion
Through this process, we demonstrated how finite normal mixtures can be used in a regression context, combined with MCMC for parameter estimation. By simulating data with known groupings and recovering the parameters through Bayesian inference, we can assess how well our model captures the underlying structure of the data.
Unless otherwise noted, all images are by the author.
The lowest price on Apple’s iPad mini 7 can be found at B&H and Amazon, with both retailers running a limited-time deal on the 256GB model.
Save $70 on Apple’s iPad mini 7 with 256GB capacity.
The 256GB iPad mini 7 in Space Gray can be snapped up for $529 at B&H and Amazon today, with both retailers knocking $70 off Apple’s MSRP on the Wi-Fi model.
Charles really loves his mostly-older Apple gear, but 2025 is going to be a year of change. Here’s how he gets work done at AppleInsider.
The AppleInsider weekend news hub and Zoom/podcasting studio.
I only develop and write stories for AppleInsider on the weekends, hence my Weekend Editor title. As a result, I have a pretty modest setup and workflow compared to most of the full-timers.
Versatility for travel is one of my key requirements, since I am on the road at various times of the year. Even when I’m at home, I’m often in a cafe or occasionally doing local radio as a “computer guru,” or on Zoom teaching online tech classes.
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